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Chapter 7 Triangles - RD Sharma Solutions for Class 10 Mathematics CBSE - TopperLearning

These Class 10 Maths has been prepared by experts faculty of Studyrankers who have large experience in teaching Maths and successfully helped students in cracking splutions with good marks. The concept and formulas used for each question has also been updated. It has become easier for students to understand the concept behind each questions. Maths is one of the main subjects for Class 10th students.

You need to solve the exercises given between the chapters. If you're facing any problem while solving any question in the exercises then you can take help from this page. The answer of each chapter is provided in the list. You only need to select the required chapter from the list and start reading. These Maths Class 10 Solutions are prepared by our experts ncert 10th maths chapter 4 solutions res are experienced and well qualified who have prepared step by step NCERT Class 10 Maths Solutions which will help you: In knowing the areas where one is lacking.

We have touched all important points and detailed ncwrt so students can easily get. NCERT Maths solutions also includes concept specific to the questions so you don't have to roam around the ncert 10th maths chapter 4 solutions res sources to understand the question. The Class 10th Maths textbook consists of total 15 chapters which can be divided mcert seven units.

These NCERT questions are important for the purpose of examinations and also help in developing your knowledge. Class 10 Maths NCERT Solutions will prove a useful guide in the development of problem solving skills and knowing how to use formulas effectively. We will start with number system and then move towards algebra. After which we will study coordinate geometry.

We will also study concepts of trigonometry and mensuration. Lastly, we will study Ncert 10th maths chapter 4 solutions res and Probability.

NCERT Solutions for Class 10 Maths It is important to note that in academic session, CBSE decided to reduce syllabus by 30 percent however many topics which have been removed can act as connectors so a students must read those topics and improve their knowledge and skills.

These are not only essential in Class 10 but if you're opting Science stream then also these topics will come so you must have proper understanding of. In the first exercise, there are four questions and most of them are based on Euclid's division lemma.

The third exercise has three questions in which you prove numbers rational or irrational. The last ncert 10th maths chapter 4 solutions res also has three questions based in which you have to expand fractions into decimals and write decimals in their fraction form. Finding accurate and step soluions step Class 10 Maths Solutions can be really tough that is why Studyrankers experts have prepared them so you can get them easily without wasting your time.

These solutions are arranged chapterwise and exercise wise as. You can use these solutions to develop your skills and knowledge. What is circumference of a circle? The total length of boundary of a circle is called circumference of a circle. What is an event in Probability? The collection of some or all possible outcomes of a random experiment is called an event. Previous Post Next Post. Contact form. LinkList ul li ul'.

Tabify by Templateify v1. Exercise 1. Exercise 2. Exercise 3. Exercise 4. Exercise 5. Solutikns 6. Exercise 7. Exercise 8. Exercise 9. Exercise

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Vessel skeleton for consultants can have small larger than a skeleton themselves, as good as the total list of equipment as well as instruments compulsory to finish your endeavour. Interjection for a recollections Nert. Here in Latest Zealand the unfit to find out correct steel club in utterly the lot of widths for my all opposite sized mitre slots upon opposite instruments.

Usually newly with extreme nert computing has it even been conceivable to try to precisely mannequin what forces have been endangered even in a single immobile state of affairs let alone in all situations.

Greek mathematician Euclid developed a geometrical approach for finding out lengths which, in our present day terminology, are solutions of quadratic equations.

Solving of quadratic equations, in general form, is often credited to ancient Indian mathematicians. In fact, Brahmagupta A. An Indian Mathematician Sridharacharya A.

Vedic Maths is very effective to improve calculation. Use Vedic Maths to make your calculation easier and faster than ever. Class 10 Maths Exercise 4. Find the original cost price of the book. How long is the piece and what is the original rate per metre?

Five articles were found damaged. Find the number of articles he bought. Find its usual speed. Find the rate at which he walking. Find the value of n. But, x cannot be negative as it is the number of articles. Therefore, and the cost of each article. Hence, the number of articles is 6 and the cost of each article is Rs. Q1 i Find the roots of the following quadratic equations, if they exist, by the method of completing the square.

Given equation:. On dividing both sides of the equation by 2, we obtain. Q1 ii Find the roots of the following quadratic equations, if they exist, by the method of completing the square. Adding and subtracting in the equation, we get. Q1 iii Find the roots of the following quadratic equations, if they exist, by the method of completing the square. On dividing both sides of the equation by 4, we obtain. Hence there are the same roots and equal:.

Q2 iv Find the roots of the following quadratic equations, if they exist, by the method of completing the square. Here the real roots do not exist in the higher studies we will study how to find the root of such equations. Q2 Find the roots of the quadratic equations given in Q.

The general form of a quadratic equation is : , where a, b, and c are arbitrary constants. Hence on comparing the given equation with the general form, we get. And the quadratic formula for finding the roots is:. Substituting the values in the quadratic formula, we obtain. Therefore, the real roots are:. Here the term inside the root is negative. Therefore there are no real roots for the given equation.

Q3 i Find the roots of the following equations:. So, simplifying it,. Comparing with the general form of the quadratic equation: , we get. Now, applying the quadratic formula to find the roots:.

Therefore, the roots are. Q3 ii Find the roots of the following equations:. Can be written as:. Hence the roots of the given equation are:. Find the present age. Let the present age of Rehman be years. Then, 3 years ago, his age was years. Then according to the question we have,. Simplifying it to get the quadratic equation:.

Hence the roots are:. However, age cannot be negative. Therefore, Rehman is 7 years old in the present. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been Find her marks in the two subjects. Let the marks obtained in Mathematics be 'm' then, the marks obtain in English will be 'm'. Then according to the question:.

Simplifying to get the quadratic equation:. Solving by the factorizing method:. We have two situations when,. Q6 The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field. Let the shorter side of the rectangle be x m. Then, the larger side of the rectangle wil be.

Diagonal of the rectangle:. It is given that the diagonal of the rectangle is 60m more than the shorter side. Hence, the roots are:. But the side cannot be negative. Hence the length of the shorter side will be: 90 m.

Q7 The difference of squares of two numbers is The square of the smaller number is 8 times the larger number. Find the two numbers. Given the difference of squares of two numbers is Let the larger number be 'x' and the smaller number be 'y'.

Then, according to the question:. On solving these two equations:. As the negative value of x is not satisfied in the equation:.

Hence, the larger number will be 18 and a smaller number can be found by,. Therefore, the numbers are or. Q8 A train travels km at a uniform speed. Find the speed of the train. Let the speed of the train be. Then, time taken to cover will be:. According to the question,. Making it a quadratic equation. Now, solving by the factorizing method:.

However, the speed cannot be negative hence,. The speed of the train is. Q9 Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately.

Find the time in which each tap can separately fill the tank. Let the time taken by the smaller pipe to fill the tank be. Then, the time taken by the larger pipe will be:. The fraction of the tank filled by a smaller pipe in 1 hour:. The fraction of the tank filled by the larger pipe in 1 hour. Given that two water taps together can fill a tank in hours. Making it a quadratic equation:.

Hence the roots are. As time is taken cannot be negative:. Therefore, time is taken individually by the smaller pipe and the larger pipe will be and hours respectively. Q10 An express train takes 1 hour less than a passenger train to travel km between Mysore and Bangalore without taking into consideration the time they stop at intermediate stations.

Let the average speed of the passenger train be. Given the average speed of the express train. Can be written as quadratic form:. Roots are:. As the speed cannot be negative. Therefore, the speed of the passenger train will be and. The speed of the express train will be. Q11 Sum of the areas of two squares is m 2. If the difference of their perimeters is 24 m, find the sides of the two squares. Let the sides of the squares be.

NOTE: length are in meters. And the perimeters will be: respectively. Areas respectively. It is given that,. Solving both equations:. Here the roots are:. As the sides of a square cannot be negative. Therefore, the sides of the squares are and. Q1 i Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:.

For a quadratic equation, the value of discriminant determines the nature of roots and is equal to:. Given the quadratic equation,. Comparing with general to get the values of a,b,c. Finding the discriminant:.

Here D is negative hence there are no real roots possible for the given equation. Q1 ii Find the nature of the roots of the following quadratic equations. The roots are given by the formula. So the roots are.

Q1 iii Find the nature of the roots of the following quadratic equations. The value of the discriminant. Therefore the given quadratic equation has two distinct real root. Q2 i Find the values of k for each of the following quadratic equations so that they have two equal roots. For two equal roots for the quadratic equation:. Comparing and getting the values of a,b, and, c. The value of. Q2 ii Find the values of k for each of the following quadratic equations so that they have two equal Ncert Solutions Of Class 10th Maths Chapter 9 Result roots.

But is NOT possible because it will not satisfy the given equation. Hence the only value of is 6 to get two equal roots. Q3 Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is m 2? If so, find its length and breadth. Let the breadth of mango grove be. Then the length of mango grove will be. And the area will be:. Which will be equal to according to question. Comparing to get the values of. Finding the discriminant value:.

Therefore, the equation will have real roots. And hence finding the dimensions:. As negative value is not possible, hence the value of breadth of mango grove will be 20m. And the length of mango grove will be:.

Q4 Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years.

Four years ago, the product of their ages in years was Let the age of one friend be. According to the question, the product of their ages in years was Now, comparing to get the values of. Discriminant value. Therefore, there are no real roots possible for this given equation and hence,.

This situation is NOT possible. Q5 Is it possible to design a rectangular park of perimeter 80 m and area m 2? Let us assume the length and breadth of the park be respectively. Then, the perimeter will be. The area of the park is:. Given :. Comparing to get the values of a, b and c. Therefore, this equation will have two equal roots. And hence the roots will be:. Therefore, the length of the park,.

When you complete the first step then your next target should be previous papers. You can pick past year papers and practice them thoroughly. Once you complete NCERTs and previous year papers, try to solve the questions of that particular chapter Ncert Solutions Class 10th Maths Chapter 2 Institution from different state board books.

NCERT solutions for class Answer: CBSE doesn't provide the marks distributions chapter-wise but it provides the total weightage of a unit upto chapters. As per CBSE the total weightage of algebra 4 chapters is 20 marks in the final board exam. Answer: Representation of statement in a quadratic equation, solving a quadratic equation using different methods, solving a quadratic equation using the "Sridharacharya" formula, sum and product of roots in a quadratic equation are important topics in this chapter.

According to guidelines of CBSE, minimum age to appear for class x must be 14 years. There is no upper limit to appear for class x cbse board. Some candidates give private exams or sometimes students fail in standard ix then they privately appear for class x then their age must be more than 14 years.

Sometimes students appear for x class after one year gap of passing class ix then also their age would be 15 or 16 as there is no upper limit age. Hello sir I'm sorry to inform you but now you're not eligible to fill the registration form as last date to fill the registration Form was 9th December Yes examination gets postponed to May but portal to fill the registration form is not open , in case if the registration form portal will open again you can fill the registration form and make the Ncert Solutions Of Class 10th Maths Chapter 7 Facebook payment.

There you can get all the papers. Solving the previous year papers, will be very beneficial for you. So, solve as much papers as you can. As per the latest CBSE Class 10 exam pattern , the theory paper will be of 80 marks, while 20 marks will be for internal assessment. To know more about exam pattern, please visit the link given below. The 10th CBSE board exam will be conducted in offline mode only, These board exams will not be conducted in online mode.

Central Board of Secondary Education conducts class 10th board examination for regular and private students. Candidates can fill CBSE 10th application form online on cbse.

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Table of contents. Therefore, can be written as: i. Q1 ii Check whether the following are quadratic equations : Answer: Given equation can be written as: i. Q1 iii Check whether the following are quadratic equations : Answer: L. S can be written as: i. Q1 iv Check whether the following are quadratic equations : Answer: L. Q1 v Check whether the following are quadratic equations : Answer: L. Q1 vi Check whether the following are quadratic equations : Answer: L.

Q1 vii Check whether the following are quadratic equations : Answer: L. Q1 viii Check whether the following are quadratic equations : Answer: L. Answer: Given the area of a rectangular plot is. Therefore the area will be: which is equal to the given plot area.

Answer: Given the product of two consecutive integers is Let two consecutive integers be and. Then, their product will be: Or. Answer: Let the age of Rohan be years. After three years, Rohan's age will be years and his mother age will be years. Then according to question, The product of their ages 3 years from now will be: Or Hence, the age of Rohan satisfies the quadratic equation. The time taken will be If the speed had been less, the time taken would be:.

Now, according to question Dividing by 3 on both the side Hence, the speed of the train satisfies the quadratic equation. Q1 ii Find the roots of the following quadratic equations by factorization: Answer: Given the quadratic equation: Factorisation gives, Hence, the roots of the given quadratic equation are.

Q1 iii Find the roots of the following quadratic equations by factorization: Answer: Given the quadratic equation: Factorization gives, Hence, the roots of the given quadratic equation are. Q1 iv Find the roots of the following quadratic equations Ncert Solutions Of Class 10th Maths Chapter 4 Exercise 4.3 Video by factorization: Answer: Given the quadratic equation: Solving the quadratic equations, we get Factorization gives, Hence, the roots of the given quadratic equation are.

Q1 v Find the roots of the following quadratic equations by factorization: Answer: Given the quadratic equation: Factorization gives, Hence, the roots of the given quadratic equation are. Answer: Let two numbers be x and y. Answer: Let the two consecutive integers be Then the sum of the squares is Answer: Let the length of the base of the triangle be.

Applying the Pythagoras theorem; we get So, Or But, the length of the base cannot be negative. Therefore, we have Altitude length and Base length. Answer: Let the number of articles produced in a day The cost of production of each article will be Given the total production on that day was. Hence we have the equation; But, x cannot be negative as it is the number of articles.

Therefore, and the cost of each article Hence, the number of articles is 6 and the cost of each article is Rs. Q1 ii Find the roots of the following quadratic equations, if they exist, by the method of completing the square Answer: Given equation: On dividing both sides of the equation by 2, we obtain Adding and subtracting in the equation, we get.

Q1 iii Find the roots of the following quadratic equations, if they exist, by the method of completing the square Answer: Given equation: On dividing both sides of the equation by 4, we obtain Adding and subtracting in the equation, we get Hence there are the same roots and equal:.

Q2 iv Find the roots of the following quadratic equations, if they exist, by the method of completing the square Answer: Given equation: On dividing both sides of the equation by 2, we obtain Adding and subtracting in the equation, we get Here the real roots do not exist in the higher studies we will study how to find the root of such equations.

Answer: i The general form of a quadratic equation is : , where a, b, and c are arbitrary constants. Hence on comparing the given equation with the general form, we get And the quadratic formula for finding the roots is: Substituting the values in the quadratic formula, we obtain Therefore, the real roots are: ii The general form of a quadratic equation is : , where a, b, and c are arbitrary constants.

Hence on comparing the given equation with the general form, we get And the quadratic formula for finding the roots is: Substituting the values in the quadratic formula, we obtain Therefore, the real roots are: iii The general form of a quadratic equation is : , where a, b, and c are arbitrary constants.

Hence on comparing the given equation with the general form, we get And the quadratic formula for finding the roots is: Substituting the values in the quadratic formula, we obtain Therefore, the real roots are: iv The general form of a quadratic equation is : , where a, b, and c are arbitrary constants.

Hence on comparing the given equation with the general form, we get And the quadratic formula for finding the roots is: Substituting the values in the quadratic formula, we obtain Here the term inside the root is negative Therefore there are no real roots for the given equation.

Q3 i Find the roots of the following equations: Answer: Given equation: So, simplifying it, Comparing with the general form of the quadratic equation: , we get Now, applying the quadratic formula to find the roots: Therefore, the roots are.

Q3 ii Find the roots of the following equations: Answer: Given equation: So, simplifying it, or Can be written as: Hence the roots of the given equation are:.

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