2025 AMC 10A Problem 3
Problem 3 of 25EasierGeometry
How many isosceles triangles are there with positive area whose side lengths are all positive integers and whose longest side has length
Answer choices
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Solution
Split into two cases. Say two sides both equal Then the third side can be any integer from to which is triangles. Now suppose is the unique longest side. The two equal legs must satisfy by the triangle inequality, and So runs from to giving triangles. Adding up, Thus, D is the correct answer.