Question

three numbers are in the ratio 2:3:4 . if the sum of the squares of the extremes is 180 , then find middle number

Answer 1

Let the extremes be 2x and 4x.
According to the question,
(2x×2x)+(4x×4x)=180
4x square + 16x square=180
20x square=180
X square=180÷20
X= root 9
X=3

There for the middle non = 3x = 3×3 = 9

Answer 2

Given :

Three numbers are in ratio 2:3:4

The sum of squares of extreme is 180.

To find : The middle number.

Solution :

Three numbers are in ratio 2:3:4 so let's assume that the numbers are 2x, 3x and 4x.

We are given that sum of squares of extreme is 180.

HERE 2 and 4 are extreme so according to the given condition the equation will be

( 2x)² + (4 x) ² = 180

taking squares we get

4x ² + 16 x² =180

solving we get

20 x² =180

x² = 180 / 20

x² = 9

x =3

putting value of x in the terms

2x = 2 x3 =6

3x = 3 x3 = 9

4 x = 4 x3 = 12

Hence the numbers are 6, 9 and 12. The middle number is 9.