Question

A rectangle is inscribed in a circle of radius 2. Find a function that represents the area of the rectangle in terms of x.

I have
(x^2)(y^2)=4 Pythagorean Theorem
(y^2)=4-(x^2)
y=sqrt(4-(x^2))
A=bh or A=xy
A=2x*2sqrt(4-(x^2))

Is this correct or what am I doing wrong?

Answer 1

the diagonal of the rectangle is a diameter of the circle. Since that is 4, if the rectangle has one side of length x, then the other side has length √(16-x^2)

So, the area is x√(16-x^2)

Well, that is not a choice, so if the side is 2x, rather than x, the area is

(2x)√(16-4x^2)
= 4x√(4-x^2)

You are correct.

Answer 2

Thank you