If three positive numbers are in the ratio 2:3:5 and the sum of their squares is 1368, then what is sum of the numbers?

Explanation

Let the numbers be 2x, 3x, and 5x. Sum of squares is (2x)^2+(3x)^2+(5x)^2 = 38x^2 = 1368, which yields x^2=36 \implies x=6. The sum of the numbers is 10x = 10(6) = 60.

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