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Question
Two positive numbers are in the ratio 3: 4 and the sum of their squares is 1225. Find the numbers.
Solution
Let the two numbers be ::lx and 4x, since the ratio between them is 3:4
Now,
(3x)2 + (4x)2 = 1225
⇒ 9x2 + 16x2 = 1225
⇒ 25x2 = 1225
⇒ x2 = 49
⇒ x = 7
∴ 3x = 21
4x = 28
Therefore, the two numbers are 21 and 28.
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