CALCULUS QUESTION HELP:(

Question

A rectangle is inscribed in a circle as shown. The diameter of the circle and the diagonal of the rectangle are both 8 meters. A. Express the length of the side y of the rectangle as a function of the side labeled x. B. Write an expression to represent the area of the rectangle, A(x).

Answer 1

8 meter diameter of a circle

inscribed is a rectangle with diagonal = 8 meters

what are the sides of the rectangle?

IF it's a square, then the diagonal of the square = the diameter of the circle. then the side of the square = 4sqr2

8^2 = (4sqr2)^2 + (4sqr2)^2 = 16(2)+ 16(2) = 16(4) = 64

Area of the rectangle (square) = a side squared = (4sqr2)^2 = 32 m^2

area of the circle is pi(r)^2 = pi(4)^2 = 16pi = about 16(3.14) = about 50 m^2 > 32 m^2, so it looks in the right general range.