The ratio of two positive numbers is 3 : 4. The sum of their

The ratio of two positive numbers is 3 : 4. The sum of their squares is 400. What is the sum of the numbers ?

Let two positive numbers be 3x and 4x.
According to the question,
(3x)² + (4x)² = 400
⇒ 9x² + 16x² = 400
⇒ 25x² = 400

⇒ x² =	400	= 16
	25

⇒ x = √16 = 4
∴ Sum of numbers
= 3x + 4x = 7x
= 7 × 4 = 28