Question 286089: The width of a rectangle is two less than its length. If the area is 48 cm squared, what are the measures of the rectangle's length and width?
Answer by mgmoeab(37)   (Show Source):
You can put this solution on YOUR website! Given:
A= 48cm²
W = L - 2
You know the area of a rectangle is A = W x L
Now, you can say:
48cm² = W x L
Substituting:
48cm² = (L - 2) L
You end up with a quadratic equation:
L² - 2L - 48 = 0
You can write this as:
L² - 8L + 6L - 48 = 0
(L² - 8L) + (6L - 48) = 0
L(L - 8) + 6 (L - 8) = 0
(L - 8)(L + 6) = 0
For this product to be true, one of them must be zero, so:
L - 8 = 0 ; L = 8
L + 6 = 0 ; L = -6 ** WE NEGLECT THE NEGATIVE ROOT.
Now that we have the length of the rectangle, we substitute this in W = L - 2, and:
W = 8 - 6 = 2
w = 8 - 2 = 6
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