The owner of a garden supply store wants to construct a fence to enclose a recta

Question

The owner of a garden supply store wants to construct a fence to enclose a rectangular outdoor storage area by using part of one side of the store, which is 250 feet long, as one of the sides of the enclosed area. There are 420 feet of fencing available for the other three sides of the enclosure. Find the dimensions of the outdoor enclosure with the most area. Note: The answer to this problem requires that you enter the correct units.

Length of side parallel to store wall =

Length of a side perpendicular to store wall =

Explanation / Answer

First thing's first... a square IS a rectangle. Don't let anybody tell you differently. Now on to your problem.

We can allow a little bit of overhang from the store. The store is 250 ft long. We will call the width x, and the length y.

The perimeter is just P = 2(x + y)

However, the building is 250 ft long, and we're using that as part of the perimeter. To compensate for the extra 250 ft we're getting, we can inrease P by 250. P is the amoutn of fencing we're using. Using the building is just like giving up 250 ft more fencing.


P + 250 = 2(x + y)
A = x * y

We want to maximize A when P = 420...

420 +250 = 2(x + y)
770 = 2(x+y)
385 = x + y

y = 385- x


Plug this into the area function

A = x * y = x (385 - x)
A = 385x - x

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