#### 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.

#### Solution

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

36x^{2} + 16x^{2} + 9x^{2} = 244

61x^{2} = 244

x^{2} = 4

x = ± 2

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

Thus, the numbers are 12, 8 and 6.

Is there an error in this question or solution?

Solution Three Positive Numbers Are in the Ratio 1/2 : 1/3 : 1/4. Find the Numbers If the Sum of Their Squares is 244. Concept: Quadratic Equations.