Question

The sum of the squares of three numbers which are in the ratio 2 : 3 : 4 is 725. What are these numbers?​

Answer 1

$\huge\red{Answer:-}$

Let the three numbers be 2x, 3x and 4x.

Given ,

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

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

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

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

$= > x = 5$

Now,

$2x = 2 \times 5 = 10$

$3x = 3 \times 5 = 15$

$4x = 4 \times 5 = 20$

Therefore, the numbers are 10, 15 and 20.

Answer 2

$\huge \star \underline \pink{AnsWeR}$

Let the number be x

(2x)²+(3x)²+(4x)²= 725

4x²+9x²+16x²=725

29x²=725

x²=25

x= 5

so number are 10,15,20