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

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.