Question

You have 800 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed? River X 800 - 2x The width, labeled x in the figure, is (Type an integer or decimal.) feet The length, labeled 800 - 2x in the figure, is feet. (Type an integer or decimal.) The largest area that can be enclosed is (Type an integer or decimal.) square

Answer 1

Hi,

Explanation:

Let's assume x the width, 800-2x the length

Area=(800-2x)*x=800x-2x²

`(dArea)/(dx) =800-4x=0\\\\x=(800)/(4) \\\\x=200(feet:\ the\ width)\\\\800-2x=800-2*200=400(feet:\ the\ length)\\\\Area=200*400=80000 (feet^2)\\\\`