Question 248575: a rectangle is 24 cm long and 16 cm wide. when each dimension is increased by the same amount, the area is doubled. what are the new dimensions?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! In solving word problems, always use as few unknowns as possible. Typically, this means you strive to define each unknown in terms of another.
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We also consider what we know about the figure. We are told it is a rectangle. So we know:
Perimeter = 2L + 2W
Area = L * W
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We also are told the dimensions of the base rectangle:
L = 24
W = 16
A = 24 * 16 = 384
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We also are told that if you add the same amount, say 'c', to both dimensions, then the area is doubled.
The problem does not ask us to find 'c' so perhaps that doesn't matter. We could just use ratios.
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24 * 16 = 384
which can be described as ratios
24/16 = 1.5
,so
1.5x*x = 384
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Doubling the area = 2*384 = 768
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1.5x^2 = 768
x^2 = 768/1.5 = 512
x = sqrt(512) = 22.6274 = W
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L= 1.5x = 33.9411
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Checking the area:
33.9411*22.6274 = 767.9988
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So this estimate is off by only 12 in ten thousand.
Very close indeed...
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