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Two similar right triangles have areas of 6 square inches and 150 square inches. The length of the hypotenuse of the smaller triangle is 5 inches. What is the sum of the lengths of the legs of the larger triangle?

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ab/2 = 6 ab = 12 b = 12/a ed/2 = 150 ed = 300 d = 300/e \[\frac{a}{b} = \frac{e}{d} \implies \frac{a^2}{12}=\frac{e^2}{300} \implies \frac{a}{e}=\frac{1}{5}\]
c = 5 a^2 + b^2 = 5^2 a^2 + (12/a)^2 = 25 a^2 + 144/a^2 = 25 a^4 + 144 = 25a^2 a^4 - 25a^2 + 144 = 0 a = 3 or a = 4 if a = 3, then b = 4 so e = 5 * 3 = 15 d = 4 * 5 = 20 f = 5*5 = 25 15 + 20 + 25 = 60

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Other answers:

There are probably a shorter way to do it
The answer key says 35
it says legs so it shouldn't include 25 15 + 20 = 35

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