A window is composed of a semicircle placed on top of a rectangle, what are the dimensions that maximizes the area of the window you can create?

Question

A window is composed of a semicircle placed on top of a rectangle. If you have 28 ft of window framing materials for the outer frame, what are the dimensions that maximizes the area (in ft²) of the window you can create? (Round your answers to two decimal places.)

radius of semicircle = ?

width of rectangle = ?

height of rectangle = ?

I don't know how to solve this problem because my doctor didn't explain it in class but brought it up in the homework

Answer 1

This Desmos graph allows you to set the perimeter then determine the radius that generates max area.

desmos.com/calculator/zwnyovn4fx