SOLUTION: the length of a rectangle is 2 cm less than twice the width. If the area is 84 square cm, find the dimensions of the rectangle

Question 1109207: the length of a rectangle is 2 cm less than twice the width. If the area is 84 square cm, find the dimensions of the rectangle
Answer by addingup(3677) (Show Source): You can put this solution on YOUR website!
L = 2W-2
L x W = 84
substitute for L:
(2W - 2) x W = 84
2W^2 - 2W = 84
divide all sides by 2:
W^2 - W = 42
W^2 - W - 42 = 0
42 is divisible by 6 and 7 (6*7 = 42) and 6 - 7 = -1:
(W^2 + 6W) + (-7W - 42)
Factor out W from W^2 + 6W and factor out -7 from -7W - 42:
W(W + 6) - 7(W+6)
Now we have a common term on both sides, W + 6. Let's factor it out and we get:
(W+6)(W-7)
so our answer is:
W+6 or W-7
W = -6 or W = 7
------------------------
Since we are not looking for a negative number, let's try the 7:
L = 2(7) - 2 = 12
So, 7 is our width and 12 our length.
Area = L x W = 12 x 7 = 84 Correct
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