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Geometry
Level
2
Given a triangle with integral side lengths and a perimeter of 8, what is the square of its area?
The answer is 8.
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By the triangle inequality, the only set of sides that gives a perimeter of 8 is (3, 3, 2). Applying Heron's formula, we get an area of √8. Our area squared is simply (√8)^2 = 8.