Premium Online Home Tutors

3 Tutor System

Starting just at 265/hour

Answer :

Let the base of the right triangle be \(x\).

The altitude can be represented by \(x - 7\).

In a right triangle,

\(Hypotenuse^2 = Base^2 + Altitude^2\) (Pythagoras Theorem)

\(\Rightarrow 13^2 = x^2 + (x - 7)^2 \)

\(\Rightarrow 169 = x^2 + x^2 - 14x + 49 \)

\(\Rightarrow 2x^2 - 14x - 120 = 0 \)

\(\Rightarrow x^2 - 7x - 60 = 0\)

(Splitting * -7x * as * 5x - 12x *)

\(\Rightarrow x^2 + 5x - 12x - 60 = 0\)

\(\Rightarrow x(x + 5) - 12(x + 5) = 0\)

\(\Rightarrow (x - 12)(x + 5) = 0\)

The roots of this equation are the values of x for which \( (x - 12)(x + 5) = 0 \)

which are,

\( x + 5 = 0 \) or \( x - 12 = 0\)

Thus, \(x = -5\) or \(x = 12\)

Since the length of any side cannot be negative, we reject \(x = -5\).

**Thus, the length of the base is 12 cm and the length of the altitude is 12 - 7 = 5 cm. **

- Find the roots of the following Quadratic Equations by factorization. (i) \(x^2 - 3x - 10 = 0\) (ii) \(2x^2 + x - 6 = 0\) (iii) \(\sqrt{2}x^2 + 7x + 5\sqrt{2} = 0\) (iv) \(2x^2 - x + {{1} \over 8} = 0\) (v) \(100x^2 - 20x + 1 = 0\)
- Solve the following situations mathematically: (i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with. (ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs.750. We would like to find out the number of toys produced on that day.
- Find two numbers whose sum is 27 and product is 182.
- Find two consecutive positive integers, sum of whose squares is 365.
- A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If, the total cost of production on that day was Rs. 90, find the number of articles produced and the cost of each article.

- NCERT solutions for class 10 maths chapter 1 Real Numbers
- NCERT solutions for class 10 maths chapter 1 Electricity, Light , Carbon and it's compounds
- NCERT solutions for class 10 maths chapter 2 Polynomials
- NCERT solutions for class 10 maths chapter 3 Pair of linear equations in two variables
- NCERT solutions for class 10 maths chapter 4 Quadratic Equations
- NCERT solutions for class 10 maths chapter 5 Arithmetic Progressions
- NCERT solutions for class 10 maths chapter 6 Triangles
- NCERT solutions for class 10 maths chapter 7 Coordinate Geometry
- NCERT solutions for class 10 maths chapter 8 Introduction to Trigonometry
- NCERT solutions for class 10 maths chapter 9 Some Applications of Trigonometry
- NCERT solutions for class 10 maths chapter 10 Circles
- NCERT solutions for class 10 maths chapter 11 Constructions
- NCERT solutions for class 10 maths chapter 12 Areas related to circles
- NCERT solutions for class 10 maths chapter 13 Surface Areas and Volumes
- NCERT solutions for class 10 maths chapter 14 Statistics
- NCERT solutions for class 10 maths chapter 15 Probability

- NCERT solutions for class 10 science chapter 1 Chemical Reactions and Equations
- NCERT solutions for class 10 science chapter 2 Acids, Bases and Salts
- NCERT solutions for class 10 science chapter 3 Metals and Non Metals
- NCERT solutions for class 10 science chapter 4 Carbon and its Compounds
- NCERT solutions for class 10 science chapter 5 Periodic Classification of Elements
- NCERT solutions for class 10 science chapter 6 Life Processes
- NCERT solutions for class 10 science chapter 7 Control and Coordination
- NCERT solutions for class 10 science chapter 8 How do Organisms Reproduce
- NCERT solutions for class 10 science chapter 9 Heredity and Evolution
- NCERT solutions for class 10 science chapter 10 Light Reflection and Refraction
- NCERT solutions for class 10 science chapter 11 Human Eye and Colorful World
- NCERT solutions for class 10 science chapter 12 Electricity
- NCERT solutions for class 10 science chapter 13 Magnetic Effect of Electric Current
- NCERT solutions for class 10 science chapter 14 Sources of Energy
- NCERT solutions for class 10 science chapter 15 Our Environment
- NCERT solutions for class 10 science chapter 16 Management of Natural Resources