Problem:
How many right triangles have integer leg lengths and and a hypotenuse of length , where ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
By the Pythagorean Theorem we have , so
Because is an integer with is an odd perfect square between and , and there are six of these, namely, , and . Hence must be , or , and there are triangles that satisfy the given conditions.
The problems on this page are the property of the MAA's American Mathematics Competitions