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