Question

Please answer this

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

Answer 1

Solution:

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

We know that,

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

So:

$\implies$ (2x)² + (3x)² + (4x)² = 725

$\implies$ 4x² + 9x² + 16x² = 725

$\implies$ 29x² = 725

$\implies$ x² = 25

$\implies$ x = 5

Now:

First number = 2(x) = 2(5) = 10

Second number = 3(x) = 3(5) = 15

Third number = 4(x) = 4(5) = 20

Verification:

Left hand side (LHS):

$\implies$ (2x)² + (3x)² + (4x)²

$\implies$ (10)² + (15)² + (20)²

$\implies$ 100 + 225 + 400

$\implies$ 725 (RHS)

Therefore:

The numbers are 10, 15 and 20.

___________________

Answered by: Niki Swar, Goa❤️

Answer 2

(2x)² +(3x)² +(4x)² = 725

4x² +9x² +16x² = 725

29x² = 725

x² = 25

x = 5

The numbers are 10, 15 and 20.