Word problems with Area

Question

bob has 50 ft of fencing to enclose a rectangular pen. He’ll use the side of the house to one side of the pen. What dimensions will make an enclosed area of 288ft squared?

Answer 1

Let the length of a rectangle be L and its width be W.

The area of the rectangle would be L x W = 288

The fifty feet of fence is the total that can be used for the perimeter of the rectangle.

For a rectangle perimeter = 2L + 2W, but since one side is being enclosed by the barn, the equation you would use is 50 = 2L + w

Solve the perimeter equation for w: w = 50 - 2L

Substitute w into the first equation: L(50 - 2L) = 288

Distribute and set the equation equal to 0: -2L²+50L - 288 = 0

Solve by factoring, quadratic formula, or graphing.

To factor, first divide the equation by -2: L²-25L+144=0

What multiples to 144 and adds to -25? -16 and -9

Factor the equation: (L - 16)(L - 9) = 0

L = 16 or L = 9

Substitute the L values into the equation 2L + W = 50

If L = 16, then W = 18; if L = 9 then W = 32

The possible dimensions of the pen are 16x18 or 9x32.