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Question

A wire is cut into two pieces, one of length a and the other of length b. The piece of length a is bent to form an equilateral triangle, and the piece of length b is bent to form a regular hexagon. The triangle and the hexagon have equal area. What is ab?

Accepted Answer

Using the area formulas for an equilateral triangle (s^234) and regular hexagon (3s^232) with side length s, plugging a3 and b6 into each equation, we find that a^2336=b^2324. Simplifying this, we get ab=62