Question

Find the perimeter of an equilateral triangle with side length of 12 inches.

Answer 1

The rectangle will have a height of a and a width of b. Call the two line segments to the left and right of the base of the rectangle s. They are equal, you can prove this quite straightforwardly.

So, 2s + b = 12. Also s = a /tan60
substituting for s, 2a /tan60 + b = 12
2a = (12 - b)tan60
a = (12-b) tan60/2
the area of the rectangle is ab or
ab = (12 - b) * b * tan60/2

Clearly, the max value of this doesn't require the constants at the end, so we need to find the max value of 12b - b squared.

You can do this in a variety of ways, but the answer is 6. Solving for a, it's also 6. So the max rectangle is a square of side 6

Answer 2

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