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In a certain right triangle, the sum of the lengths of the

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New post 31 Mar 2004, 10:35
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In a certain right triangle, the sum of the lengths of the two legs and the hypotenuse is 60 inches. If the hypotenuse is 26 inches, which of the following is the length of one of the legs?

A. 24 inches
B. 34 inches
C. 29 inches
D. 16 inches
E. 13 inches
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New post 31 Mar 2004, 10:41
An instance of a 30-60-90 triangle
Exactly double the measurements of the 5-12-13 triangle
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New post 31 Mar 2004, 13:58
Let one leg : a
Other leg : b
Hypoteneuse : c

a+b+h = 60
a+b = 60-26 = 34

squaring both sides:

a^2 + b^2 + 2ab = 34^2

we know a^2 + b^2 = h^2 = 26^2

i.e. 26^2 + 2ab = 34^2

ab = 240 ------(1)
a+b = 34 ------(2)

Solving equations (1) and (2), we get one of the legs = 10 or 24

Hence (A) 24 inches is the answer.
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