Question 116304: Please help me with this confusing question. I have tried and I just can't seem to figure it out. PLEASE HELP ME!!!! Here is the question:
What is The area of a rectangle is 24 square meters. Find the length and width of the rectangle if its length is 2 meters greater than its width. Use an equation and the formula ® area of a rectangle = (width)(length).
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Start with the equation for the area of a rectangle ...
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Area = width*length
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or for short:
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A = W * L
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You are told that the area is 24 square meters, so substitute 24 for A to get:
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24 = W * L
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Next you are told that the length L is equal to the Width plus 2 meters. In equation form
this is:
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L = W + 2
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Return to the area equation and substitute W + 2 for L and you have:
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24 = W * (W + 2)
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Note that this equation has only 1 variable ... W. Since it only has one variable,
we have a chance of solving it. Begin by multiplying out the right side:
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24 = W^2 + 2W
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Get this into standard quadratic form by subtracting 24 from both sides to get:
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0 = W^2 + 2W - 24
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Transpose (switch) the sides of the equation to get it into the more familiar form:
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W^2 + 2W - 24 = 0
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Factor the left side:
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(W + 6)*(W - 4) = 0
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This equation will be true if one of the factors equals zero because a multiplication
by zero on the left side will make the left side equal zero and therefore equal the zero on the
right side. So set each factor equal to zero and solve for the value of W.
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W + 6 = 0
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Subtract 6 from both sides and you get W = -6. But this doesn't make sense ... a negative width???
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Set the other factor equal to zero:
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W - 4 = 0
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Add 4 to both sides and you get W = 4. That makes sense. The width is 4 meters and since
the length is 2 meters longer than the width, the length is 6 meters. If you multiply the
width (4) times the length (6) you get 24 square meters, so that checks.
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The answers are length = 6 meters and width = 4 meters.
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Hope this helps you to understand the problem.
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