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Problem 613

Given the unit length below, construct a segment of length \(\sqrt{3}\)

Expert verified

Construct an equilateral triangle with side length 1, and then another adjacent equilateral triangle with side length 2. Split the larger triangle into two smaller equilateral triangles by drawing a perpendicular from one vertex to the opposite side. Apply the Pythagorean theorem to find the length of the altitude of the larger triangle, which is \(\sqrt{3}\).

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