2008 AMC 10B Problems/Problem 15

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

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 $\boxed{A}$ .

2008 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
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