Expert: Steve Holleran - 5/14/2007

Question
A rectangle is inscribed in a circle of a diameter 33 in . Express p the perimeter of the rectangle as a function of L its length

Answer
Hello Dawn,

Okay, this won't be so bad.  If you call the length L and the width W, then when you inscribe the rectangle in the circle, and draw one of its diagonals, this diagonal is the diameter of the circle.  So if you use the Pythagorean Theorem on one of the triangles formed, you have :

          L^2 + W^2 = 33^2 = 1089

or               W^2 = 1089 - L^2

or               W = sqrt(1089 - L^2)


Now the perimeter is P = 2L + 2W, and if you substitute the expression above for W, you have

                P = 2L + 2 * sqrt(1089 - L^2)

Its not pretty, but it does give P as a function of L.

Hope this helps out.


Steve Holleran