perplexus.info :: Just Math : Rectangle in a circle

Rectangle in a circle (Posted on 2017-11-07)

What is the maximum perimeter
of a rectangle inscribed in
a half of a circle with radius R?

No Solution Yet Submitted by Ady TZIDON

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Another calculus solution

| Comment 2 of 4 |

Let the height of the rectangle be h.

Then the perimeter = 2h+4sqrt(R^2-h^2).

The derivative with respect to h = 2 - 4h/sqrt(R^2-h^2).

Set this equal to 0 and solve for h,

yielding h = R/sqrt(5)

Then the perimeter =

2R/sqrt(5) + 4sqrt(4R^2/5) = 10R/sqrt(5) = 2R*sqrt(5)

Posted by Steve Herman on 2017-11-07 12:19:28

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