Question

Two numbers are in the ratio of 3 : 5 and the sum of their squares is 1666. Find them.

Answer 1

Let the two numbers be:

3x and 5x

(3x)² + (5x)² = 1666

9x² + 25x² = 1666

34x² = 1666

x² = `1666/34`

x² = 49

x = `sqrt49`

x = 7

Find the actual numbers:

3x = 3 × 7 = 21

5x = 5 × 7 = 35

The two numbers are 21 and 35.