A reference to HOMC
Geometry
Level
pending
Find all the right triangles satisfying the following conditions:
- They have integer side lengths.
- The area is equal to the perimeter.
Submit your answer as the sum of the areas of those triangles.
The answer is 54.
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1 solution
The triangles that can be found are the 6 − 8 − 1 0 triangle and the 5 − 1 2 − 1 3 triangle. You can verify those by yourself.
The 6 − 8 − 1 0 has an area of 24, and the 5 − 1 2 − 1 3 has an area of 30. Their sum is 2 4 + 3 0 = 5 4 .