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Question
Find three numbers in the ratio 2 : 3 : 5, the sum of whose squares is 608.
Solution
Let the numbers be 2x, 3x and 5x
According to question,
(2x)2 + (3x)2 + (5x)2 = 608
⇒ 4x2 + 9x2 + 25x2 = 608
⇒ 38x2 = 608
⇒ `x^2 = 608/38 = 16`
⇒ `x = sqrt(16)`
Now, 16 = 2 × 2 × 2 × 2 = (2 × 2)2
⇒ `sqrt(16) = 2 xx 2 = 4`
∴ `x = sqrt(16) = 4`
Hence, the numbers are 2 × 4, 3 × 4, 5 × 4, i.e. 8, 12 and 20.
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