Question

Find three numbers in the ratio 2 : 3 : 5, the sum of whose squares is 608.

Answer 1

Let the numbers be 2x, 3x and 5x

According to question,

(2x)² + (3x)² + (5x)² = 608 

⇒ 4x² + 9x² + 25x² = 608

⇒ 38x² = 608

⇒ `x^2 = 608/38 = 16`

⇒ `x = sqrt(16)` 

Now, 16 = 2 × 2 × 2 × 2 = (2 × 2)²

⇒ `sqrt(16) = 2 xx 2 = 4`

∴ `x = sqrt(16) = 4`

Hence, the numbers are 2 × 4, 3 × 4, 5 × 4, i.e. 8, 12 and 20.