Michael J. answered • 10/03/16

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Effective High School STEM Tutor & CUNY Math Peer Leader

112 feet of fence is the length of the fencing. The area of a rectangle is length times width. The perimeter of a rectangle is the sum of twice the length and twice the width.

Let length = x

Let width = y

Use these variables to create equations.

2(x + y) = 112 eq1

**x + y = 56 eq1**

**Area = xy eq2**

Substitute eq1 into eq2 to get a function area in terms of only x and y.

Area = x(56 - x)

Area = -x

^{2}+ 56xThe area represents a parabola that opens downward. What you need to do is find the vertex of this parabola.

Find the x-coordinate of the vertex using this formula:

x = -b / (2a)

**where:**

a = -1

b = 56

Plug in these values into the formula. Then evaluate the area at that x-coordinate. That will be your maximum area.