# The difference of squares of two numbers is 180. The square of a smaller number is 8 times the larger number. Find the two numbers.

**Solution:**

Let the larger number be x.

The square of the smaller number is 8 times the larger number = 8x.

Given that the difference of squares of the two numbers is 180.

Square of larger number - Square of smaller number = 180

x^{2} - 8x = 180

x^{2} - 8x - 180 = 0

x^{2} - 18x + 10x - 180 = 0

x(x -18) + 10(x - 18) = 0

(x -18)(x + 10) = 0

x - 18 = 0 and x + 10 = 0

x = 18 and x = - 10

If the larger number is 18, then square of smaller number = 8 × 18

Therefore, smaller number = ± √8 × 18

= ± √ (2 × 2 × 2 × 3 × 3 × 2)

= ± (2 × 2 × 3)

= ± 12

If larger number is - 10, then square of smaller number = 8 × (- 10) = - 80

The square of any number cannot be negative.

Therefore, x = -10 is not applicable.

The numbers are 18, 12 (or) 18, - 12.

**ā Check: **NCERT Solutions for Class 10 Maths Chapter 4

**Video Solution:**

## The difference of squares of two numbers is 180. The square of a smaller number is 8 times the larger number. Find the two numbers

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.3 Question 7

**Summary:**

The difference of squares of the two numbers is 180. If the square of a smaller number is 8 times the larger number then the two numbers are 12, 18 or -12, 18.

**ā Related Questions:**

- A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.
- Two water taps together can fill a tank in 9 3/8 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?
- An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of an express train is 11km /hr more than that of a passenger train, find the average speed of the two trains.
- Sum of the areas of two squares 468 m^2. If the difference of their perimeters is 24m, find the sides of the two squares.

visual curriculum