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Smurfsnot2604 · May 31, 2009, 06:41 AM

A rectangle is inscribed in a semicirlce with a radius of 50. Find a function that models the area A of the rectangle in terms of it's height.

If someone can help me step by step I would greatly appreciate it

galactus · May 31, 2009, 07:31 AM

Per the diagram, the area of the rectangle is A=xy.

But, by Pythagoras, $(\frac{x}{2})^{2}+y^{2}=50^{2}$

y is the height, so we can solve this equation for x and sub into the area formula.

$x=2\sqrt{2500-y^{2}}$

Sub into A:

$A=2y\sqrt{2500-y^{2}}$

There, the area is in terms of its height, y.