SOLUTION: the length of a rectangle is 6 cm less than twice its width. find the dimintions of the rectangle if its area is 108 cm2

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Question 553041: the length of a rectangle is 6 cm less than twice its width. find the dimintions of the rectangle if its area is 108 cm2
Answer by TutorDelphia(193) About Me  (Show Source):
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the length of a rectangle is 6 cm less than twice its width can be written as:
l=2%2Aw-6
And using the area formula of a rectangle we know that
l*w=108
Using subsitution we can plug in (2*w-6) for the length
%282%2Aw-6%29%2Aw=108
Distribute
2w%5E2-6w=108
Divide both sides by 2
w%5E2-3w=54
subtract 54 from both sides
w%5E2-3w-54=0
factor
(w-9)(w+6)=0
w=9 or -6
Discard the negative number because negatives don't exist with distances
w=9
Now that we know w we can find l
l=2*w-6
Sub in 9 for w
l=2*9-6
l=18-6
l=12