Question

The perimeter of a rectangle is 110 meters and the length is 25 meters longer than the width. find the dimensions of the rectangle. let x= the length and y= the width. the corresponding modeling system is {2x+2y=110x−y=25. solve the system graphically.

Answer 1

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Define x and y:
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Length = x
Width = y

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Construct the two equations:
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The perimeter is 110:
2x + 2y = 110

The Length is 25m longer than the width:
x = y + 25

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Solve x and y:
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2x + 2y = 110 ---------------- (1)
x = y + 25 ---------------------(2)

Substitute (2) into (1):

2x + 2y = 110
2( y + 25) + 2y = 110
2y + 50 + 2y = 110
4y + 50 = 110
4y = 110 - 50
4y - 60
y = 15m

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Substitute y=15 into equation 1:
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x = y + 25
x = 15 + 25
x = 40m

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Find Length and Width:
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Length = x = 40m
Width = y = 15m

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Answer: Length = 40m , Width = 15m
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