Math CentralQuandaries & Queries


Question from Niki, a student:
Consider a rectangle inscribed in a circle with a radius or R. What are the possible perimeters for the rectangle?
Hi Niki.

The best way to approach this is to center the circle on the origin of a normal graph and use x as your independent variable.

Now it should be clear to you that the perimeter is simply 4(x+y). Thus, we really only need to think about the first quadrant.

x varies from 0 to R, of course, and so does y. But you can express f(x) = y by re-arranging the circle's equation

R2 = x2 + y2.

Then just find the minimum and maximum values of the expression x + f(x) and multiply by four.

Write back if you need more hints.

Stephen La Rocque.

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