Question

Three numbers are in the ratio `(1)/(2) : (1)/(3) : (1)/(4)` If the sum of their squares is 244, find the numbers.

Answer 1

The ratio of three numbers `(1)/(2) : (1)/(3) : (1)/(4)` 

= `(16 : 4 : 3)/(12)`
= 6 : 4 : 3
Let first number 6x, second 4x and third 3x
∴ According to the condition
(6x)² + (4x)² + (3x)² = 244
⇒ 36x² + 16x² + 9x² = 244
⇒ 61x2 = 244
⇒ x 2 = `(244)/(61)`
= 4 = (2)²
∴ x = 2
∴ first number = 6x = 6 x 2 = 12
second number = 4x = 4 x 2 = 8
and third number = 3x = 3 x 2 = 6.