2008 AMC 10B Problems/Problem 15

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Problem

How many right triangles have integer leg lengths a and b and a hypotenuse of length b+1, where b<100?

(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

Solution

By the pytahagorean theorem, $a^2+b^2=b^2+2b+1$

This means that $a^2=2b+1$.

We know that $a,b>0$, and that $b<100$.

We also know that a must be odd, since the right

side is odd.

So $a=3,5,7,9,11,13$, and the answer is $\boxed{A}$.

See also

2008 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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All AMC 10 Problems and Solutions
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