Problem:
How many non-congruent right triangles with positive integer leg lengths have areas that are numerically equal to 3 times their perimeters?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the triangle have leg lengths and , with . The given condition implies that
so
Squaring both sides and simplifying yields
from which
The positive integer solutions of the last equation are , , and . However, the solution is extraneous, and there are right triangles with the required property.
The problems on this page are the property of the MAA's American Mathematics Competitions