Michael M. answered • 04/10/21

Math, Chem, Physics, Test Prep Tutoring with Michael ("800" SAT math)

One condition is the boundary is 500 feet long. Let d be the diameter of the semicircles and w be the width of the rectangle. Then we get the equation πd + 2w = 500 for our condition.

We're trying to maximize the area of the rectangle and the area of the rectangle = w*d.

Solve for w in the condition:

w = (500 - πd)/2

Then plug this into the function we're maximizing

Area = (500 - πd)/2 * d.

Find the absolute maximum value of this on the interval d ≥ 10

Do you think you'll be able to do this?