2008 AMC 10B Problems/Problem 15
Problem
How many right triangles have integer leg lengths and and a hypotenuse of length , where ?
Solution
By the Pythagorean theorem,
This means that .
We know that and that .
We also know that is odd and thus is odd, since the right side of the equation is odd. is even. is odd.
So , but if , then . Thus
The answer is .
~qkddud (edited by aopsthedude and bburubburu)
Video Solution by OmegaLearn
https://youtu.be/euz1azVKUYs?t=135
~ pi_is_3.14
See also
2008 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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All AMC 10 Problems and Solutions |
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