Question 144667
The sum of the legs of a right triangle is 17 in. The longer leg is 2 more than twice the shorter. The hypotenuse is 13 in. Find the length of each leg. 
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Isn't the formula for a right triangle a^2 +b^2 = c^2?  Yes it is, but we don't need it here.
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It says,"The hypotenuse is 13 in." therefore
c = 13
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Let a = shorter leg
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then it says,"The longer leg is 2 more than twice the shorter."therefore
b = 2a+2
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"the sum of the legs of a right triangle is 17":
a + b = 17
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Substitute (2a+2) for b and 13 for c, find a:
a + (2a+2) = 17
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3a + 2 = 17
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3a = 17 - 2
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3a = 15
a = {{{15/3}}}
a = 5
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Find the longer leg (b):
b = 2(5) + 2
b = 12
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We can confirm our solution using the pythag
Does 5^2 + 12^2 = 13^2?