A rectangle is inscribed in a semicircle of radius 2. Let P = (x,y) be the point in quadrant 1 that is a vertex of the rectangle and is on the circle.
(a) Express the area A of the rectangle as a function of x.
(b) Express the perimeter p of the rectangle as a function of x.
Hello,
the circle line of the semicircle is described by:
according to Pythagorean theorem.
If the height of the rectangle isy then the length of the rectangle is 2x.
The area of a rectangle can be calculated by:
Plug in the terms of length and height:
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EDIT: I forgot to show you how to calculate the perimeter of the rectangle:
In general the perimeter is: P = 2*length + 2*height
Using the terms for length and height you get: