Question 446483: Monique decided to create a rectangular herb garden in her backyard. The length of the garden was 4 feet longer than its width and covered an area of 192 square feet. How many feet of fencing did she use?
Answer by Leaf W.(135)   (Show Source):
You can put this solution on YOUR website! width = w
length = w + 4
Area = width*length = w(w + 4)
Set up your equation: w(w + 4) = 192
Distribute the w into the w and 4: 
Subtract 192 from both sides: 
Factor the polynomial: (w - 12)(w + 16) = 0
Since the only way for the product of two numbers to equal zero is if one of the numbers is zero itself, one of the factors (w - 12 or w + 16) must equal zero. Find out what value of w would make each factor zero by setting each equal to zero and solving for w:
1. w - 12 = 0
Add 12 to both sides: w = 12
The width of the rectangle could be 12
2. w + 16 = 0
Subtract 16 from both sides: w = -16
However, since the width cannot be negative, -16 is not a possible answer. THEREFORE, THE WIDTH MUST BE 12 FEET.
In that case what is the length of the rectangle? Simply plug the value of 12 for w into the expression for length (w + 4): 12 + 4 = 16. THEREFORE, THE LENGTH MUST BE 16 FEET.
However, the problem is not asking for the dimensions of the rectangle; it is asking for the number of feet of fencing she used, which is the same as asking for the perimeter, as the fencing runs all around the perimeter. The equation of perimeter is 2(length) + 2(width), so you can just plug in the values for length and width that you found above: 2(16) + 2(12)
Multiply: 32 + 24
Add: 56
THEREFORE, MONIQUE USED 56 FEET OF FENCING.
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