Question

Two whole numbers are in the ratio 3 : 2. If the sum of their squares is 52, the numbers are ______.

Options

• 9 and 6

• 6 and 4

• 9 and 4

• None of these

Answer 1

Two whole numbers are in the ratio 3 : 2. If the sum of their squares is 52, the numbers are 6 and 4.

Explanation: 

It is given that two whole numbers are in ratio 3:2.

Let the numbers be 3x and 2x.

The sum of their square = 52.

⇒ (3x)² + (2x)² = 52

⇒ 9x² + 4x² = 52

⇒ 13x² = 52

⇒ x² = `52/13`

⇒ x² = 4

⇒ x = `sqrt4​`

⇒ x = ± 2

So, the numbers = 3x = 3 × 2 or 3 × (−2) = 6 or −6

2x = 2 × 2 or 2 × (−2) = 4 or −4

Since, the given numbers are whole numbers. So, the numbers cannot be −6 and −4.