SOLUTION: A rectangle is inscribed in a semicircle of radius r = 12. Find a function that models the area A of the rectangle in terms of its height h.

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Question 1035127: A rectangle is inscribed in a semicircle of radius
r = 12. Find a function that models the area A of the rectangle in terms of its height h.
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
If you draw the diagram, you can sketch in the radius 12 from the center of the circle to the corner of the rectangle. Using the Pythagorean Theorem, you can find half the base of the rectangle to be
sqrt%28144-h%5E2%29
The whole base of it is twice that. The area of the rectangle is h times THAT. Thus
A%28h%29+=+2h%2Asqrt%28144-h%5E2%29