Problem:
How many noncongruent integer-sided triangles with positive area and perimeter less than 15 are neither equilateral, isosceles, nor right triangles?
Answer Choices:
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Solution:
Let the side lengths be . By the Triangle Inequality ; it follows that perimeter . Then , , and . The only triangles (denoted by three-digit numbers with decreasing digits) that are not equilateral or isosceles are , 542 , and 432 . Of these, only 543 is a right triangle, so the answer is .
The problems on this page are the property of the MAA's American Mathematics Competitions