SOLUTION: Given 3 sides of a rectangular fence have a perimeter of 80 feet. Find the largest possible area.

Question 111370: Given 3 sides of a rectangular fence have a perimeter of 80 feet. Find the largest possible area.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
The formula for the perimeter of rectangle is , but since we have 3 sides, the formula becomes

Now set the perimeter P equal to 80

Now solve for L

Now the area of a rectangle is

Plug in

Now plot as a function of x. Simply change A to y and w to x to get

From the graph we can see that the max is at x=20, which means y=800. So when the width is 20 ft the area is maxed out at 800 square feet
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