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The area of a triangle with sides 13, 14 and 15

geometrytrianglespythagorasheron

A triangle has sides of length 13, 14 and 15.

What is its area? Find it by splitting the triangle with a height, then check with Heron's formula. Why are these three side lengths a favourite of puzzle-setters?

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Drop the height onto the side of length 14. It splits that side into two pieces, x and 14 minus x, and the height h satisfies Pythagoras in both right triangles.

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