Question 687691: The length of a rectangle is 1ft less than twice its width, and the area of the rectangle is 78 feet squared . Find the dimensions of the rectangle.
Answer by josh_jordan(263)   (Show Source):
You can put this solution on YOUR website! In order to solve, let's first convert each part of the first sentence into an equation. The first part of the sentence says "The length of a rectangle is 1 ft less than twice its width". In other words:
L = 2W - 1, where L stands for Length, and W stands for Width
The second part of the first sentence states that "the area of the rectangle is 78 feet squared". In other words:
L x W = 78
Now, in our second equation, L x W = 78, we can replace L with 2W - 1:
(2W - 1) x W = 78
Using distribution, we will multiply W by what's in the parenthesis on the left side of our equal sign, giving us:
If we subtract 78 from both sides, we will have a quadratic equation that we can use the quadratic formula to solve:
 a = 2, b = -1, c = -78
After substituting each value in the quadratic formula, we obtain a solution set of 13/2 and -6. Since the width of our rectangle cannot be negative, -6 will not work. Therefore 13/2 is our width.
To find our lengh, replace W with 13/2 in our first equation, L = 2W - 1:
 =
 = 12
Therefore, our length is 12 feet and our width is 13/2 or 6.5 feet.
We can validate by multiplying these two numbers together, which will give us 78.
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