Question

The sum of the Squares of three positive integers which are in the ratio 2:3:4 is 725 find integers.

Answer 1

Answer :

Let the numbers be 2x, 3x & 4x respectively.

Therefore, according to question :

$( {2x})^{2} + ( {3x})^{2} + ( {4x})^{2} = 725$

$=> \: {4x}^{2} + {9x}^{2} + {16x}^{2} = 725$

$=> \: {29x}^{2} = 725$

$=> \: {x}^{2} = \frac{725}{29}$

$=> \: {x}^{2} = 25$

$=> \: x = 5$

Therefore, the numbers are :

2x = 2*5 = 10

3x = 3*5 = 15

4x = 4*5 = 20