MATH SOLVE

2 months ago

Q:
# 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.

Accepted Solution

A:

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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

------------------------------------------------

Answer: Length = 40m , Width = 15m

------------------------------------------------

Define x and y:

------------------------------------------------

Length = x

Width = y

------------------------------------------------

Construct the two equations:

------------------------------------------------

The perimeter is 110:

2x + 2y = 110

The Length is 25m longer than the width:

x = y + 25

------------------------------------------------

Solve x and y:

------------------------------------------------

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

------------------------------------------------

Substitute y=15 into equation 1:

------------------------------------------------

x = y + 25

x = 15 + 25

x = 40m

------------------------------------------------

Find Length and Width:

------------------------------------------------

Length = x = 40m

Width = y = 15m

------------------------------------------------

Answer: Length = 40m , Width = 15m

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