SOLUTION: The width of a rectangle is 1cm more than half the length. When both the length and the width are increased by 1cm, the area increases by 20cm^2. Find the original dimensions of th

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Question 769978: The width of a rectangle is 1cm more than half the length. When both the length and the width are increased by 1cm, the area increases by 20cm^2. Find the original dimensions of the rectangle.
Answer by stanbon(75887) About Me  (Show Source):
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The width of a rectangle is 1cm more than half the length. When both the length and the width are increased by 1cm, the area increases by 20cm^2. Find the original dimensions of the rectangle.
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Original DATA:
length = L
width = (1/2)L+1
Area = (1/2)L^2 + L
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New DATA:
Length = L+1
width = (1/2)L+2
Area = (L+1)[(1/2)L+2]
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Equation:
New area - Old area = 20 cm^2
(L+1)((1/2)L+2) - [(1/2)L^2+L] = 20
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(1/2)L^2 + (5/2)L +2 - (1/2)L^2 - L = 20
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(7/2)L = 18
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L = 36/7 cm (original Length)
Original width = (1/2)L + 1 = (18/7)+(7/7) = 25/7 (original width)
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Cheers,
Stan H.
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