Question

Three positive numbers are in the ratio `1/2 : 1/3 : 1/4`. Find the numbers if the sum of their squares is 244.

Answer 1

Given, three positive numbers are in the ratio `1/2 : 1/3 : 1/4 = 6 : 4 : 3`

Let the numbers be 6x, 4x and 3x.

From the given information,

(6x)² + (4x)² + (3x)² = 244

36x² + 16x² + 9x² = 244

61x² = 244

x² = 4

x = ± 2

Since, the numbers are positive, so x = 2.

Thus, the numbers are 12, 8 and 6.