Math CentralQuandaries & Queries


Question from Alexea, a student:

A rectangle is inscribed in a circle of diameter 15in. Express the perimeter as a function of the width x.

Hi Alexea,

Let the height of the rectangle by $y$ then the perimeter is $2x + 2y.$

rectangle in circle

In my diagram $ABC$ is a right triangle. What does Pythagoras tell you? Solve for $y$ in terms of $x.$ Substitute into the perimeter expression.


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