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RJW RJW
wrote...
10 years ago
Find the max area of a rectangle that can be inscribed in an equilateral triangle with sides of length L. Pleas Please Please help me
to math man. This is not really a hard question to our teacher but I dont really understand optimization so could you explain how you got the answer?
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wrote...
10 years ago
I've solved it, but not using calculus:

I think we can assume one side of the rectangle is on the base of the triangle.
If you call the base of the rectangle B, then either side of the rectangle will be right-angled triangles with base A/2 (where A = L-B).
The height of these triangles, and therefore of the rectangle, is (A/2)xtan(60), which is A x (root3)/2.
So the rectangle is defined as AB x (root3)/2.
This is maximised when A and B are equal, which is when they are both L/2.

So the maximum area is L^2 x (root3)/8.
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