Question

The sum of squaresof three numberswhich are in the ratio 2:3:4 is 725 what are the numbers?

Answer 1

Answer :

• The numbers are 10 , 15 and 20

Given :

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

To find :

• The numbers

Solution

Given,

• The sum of squares of three numbers which are in the ratio 2:3:4 then

• Let the ratio be 2x , 3x and 4x

Sum is 725

Substituting the value :

⇥ 2x² + 3x² + 4x² = 725

⇥ 4x² + 9x² + 16x² = 725

⇥ 29x² = 725

⇥ x² = 725/29

⇥ x = √25

⇥ x = 5

Finding the numbers :

⇥ 2x

⇥ 2(5)

⇥ 10

⇥ 3x

⇥ 3(5)

⇥ 15

⇥ 4x

⇥ 4(5)

⇥ 20

Hence , The numbers are 10 ,15 and 20.

Verification :

⇥ 4x² + 9x² + 16x² = 725

⇥ 4(5)² + 9(5)² + 16(5)² = 725

⇥ 4 × 25 + 9 × 25 + 16 × 25 = 725

⇥ 100 + 225 + 400 = 725

⇥ 725 = 725

Hence , Verified

Answer 2

Step-by-step explanation:

Sum of Three square = 725

Ratio = 2:3:4

Square = s×s

2:3:4 = (2x)² + (3x)² + (4x)²

725 = 4x² + 9x² + 16x²

725 = 29x²

x² = 725 ÷ 29

x² = 25

x = 5

2x = 5×2 = 10

3x = 5×3 = 15

4x = 5×4 = 20