Question 243737: The area of a rectangle is 80 square feet. The length is 2 feet longer than the width. Find the measure of each. Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! We know the area of a rectangle is width times the length.
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We are told A = 80
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We also are told L is 2 feet longer than the width.
or
You pick.
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Substituting what we know:
Multiplying through the right-hand:
Equal things are equal, so we can rewrite:
Subracting 80 from both sides
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We now consider whether it can be factored. The factors of 80 are 2*40, 4*20, 5*18, 8*10...
We have to have different signs to get them to multiply to -80.
And we need them to be 2 apart to have the solve the L term. 8 & 10 is the way to go.
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So we have two candidate solutions: L=10 and L=-8.
Since we are talking about the area of a rectangle, a length of -8 is not reasonable. So we'll test 10.
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Looking back at the equations we established:
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So we propose the L=10 and W=8.
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Checking the Area, we test:
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That checks. So we're done.
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