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Question 630904:
8. The length of a rectangle is 5 meters more than its width. If the area is 66 square meters, what are the length and width?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! This problem can be solved using one variable or two. Using two variables may be a more "natural" way to solve the problem since there are two unknowns, the length and the width. But you need as many equations as you have variables. So if we use two variables we will need two equations. If we use just one variable we only need one equation.
So if it not too hard to figure out how to express both unknowns with just one variable, then that will be the easier way to go. With this problem, the first sentence tells us the exact relationship between the length and width and it is not a very complex relationship. So it looks like one variable will not be difficult.
When you are trying to express more than one number in terms of a single variable, I find it helpful to make the variable represent the lower number. By making the variable the lower number, you get to use addition and/or multiplication to express the other number(s). Addition and multiplication are inherently easier to use correctly than subtraction and division.
So
Let x = width (since it is smaller than the length).
The x+5 = length (since the length is 5 more than the width)
Now we just need one equation. This equation will come from the second sentence. This sentence mentions area. And how do we find area of a rectangle? Answer: A = l*w. We just replace the A with 66, the l with (x+5) and the w with x:
66 = (x+5)*x
Now we solve for x. First we simplify:
Since this is a quadratic equation we want one side to be zero. Subtracting 66 from each side we get:
Next we factor (or use the Quadratic Formula). This factors fairly easily:
From the Zero Product Property we know that one of the factors must be zero:
 or 
Solving these we get:
 or 
"x" represents the width of our rectangle. Since widths should not be negative, we will reject/discard the negative result. So x, the width, is 5 meters. This makes the length, x+5, 6+5 or 11 meters.
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