Question

the perimeter of a rectangle is 56 m. if the width were doubled and the length were increased by 8 m, then the perimeter would be 82 m. what are the dimensions

Answer 1

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Define x and y:
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Let the length be x.
Let the width be y.

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Formula:
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Perimeter = 2(Length + Width)

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Construct equations and solve for x and y:
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2x + 2y = 56            ---------------------- (1)
2(x+8) + 4y = 82     -----------------------(2)

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From equation 1:
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2x + 2y = 56
x + y = 28
x = 28 - y

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From equation 2:
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2(x+8) + 4y = 82 
2x + 16 + 4y = 82
2x + 4y = 66
x + 2y = 33

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Substitute x = 28 - y into equation 2:
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x + 2y = 33
(28 - y) + 2y = 33
28 - y + 2y = 33
y = 5

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Substitute y = 5 into equation 1:
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x = 28 - y 
x = 28 - 5
x = 23

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Find Length and Width
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Length = x = 23 m
Width = y = 5m

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Answer: Length = 23m and Width = 5m
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