A rectangle is inscribed in a semicircle of radius 2. Let P = (x,y) be the point in the quadrant I that is a vertex of the rectangle and is on the circle.

1) Express the area A of the rectangle as a function of x.
2) Express the perimeter p of the rectangle as a function of x.

Question

A rectangle is inscribed in a semicircle of radius 2. Let P = (x,y) be the point in the quadrant I that is a vertex of the rectangle and is on the circle.

1) Express the area A of the rectangle as a function of x.
2) Express the perimeter p of the rectangle as a function of x.

turingtest · Answer

what is the equation of the circle?

anonymous · Answer

I have the answers I just want to check them over. The equation is:

\[y = \sqrt{4 - x ^{2}})]

turingtest · Answer

|dw:1346971472892:dw|yep, good for y

turingtest · Answer

so then what is A(x) (area as a function of x) ?

anonymous · Answer

$$A(x) = x(\sqrt{4 - x ^{2}})$$

turingtest · Answer

almost, but be careful
what is the length of this side?|dw:1346971647316:dw|