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Writing Equations Given Dimensions of Shapes

1.8.4 Writing Equations Given Dimensions of Shapes

1.8.4 • Writing Equations Given Dimensions of Shapes

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The perimeter of a rectangle is 48 centimeters. The relationship between the length, the width, and the perimeter of the rectangle can be described with the equation:  2 · length + 2 · width = 48 2 · length + 2 · width = 48 .

Find the length, in centimeters, if the width is:

1.

10 centimeters

14

2 L + 2 ( 10 ) = 48 2 L + 2 ( 10 ) = 48

2 L + 20 = 48 2 L + 20 = 48

2 L + 20 − 20 = 48 − 20 2 L + 20 − 20 = 48 − 20

2 L = 28 2 L = 28

1 2 ( 2 L ) = 1 2 ( 28 ) 1 2 ( 2 L ) = 1 2 ( 28 )

L = 14 L = 14

2.

3.6 centimeters

2 L + 2 ( 3.6 ) = 48 2 L + 2 ( 3.6 ) = 48

2 L + 7.2 = 48 2 L + 7.2 = 48

2 L + 7.2 − 7.2 = 48 − 7.2 2 L + 7.2 − 7.2 = 48 − 7.2

2 L = 40.8 2 L = 40.8

1 2 ( 2 L ) = 1 2 ( 40.8 ) 1 2 ( 2 L ) = 1 2 ( 40.8 )

L = 20.4 L = 20.4

3.

w w centimeters

Compare your answer:

2 L + 2 ( w ) = 48 2 L + 2 ( w ) = 48

2 L + 2 w = 48 2 L + 2 w = 48

2 L + 2 w − 2 w = 48 − 2 s 2 L + 2 w − 2 w = 48 − 2 s

2 L = 48 − 2 2 L = 48 − 2

1 2 ( 2 L ) = 1 2 ( 48 − 2 s ) 1 2 ( 2 L ) = 1 2 ( 48 − 2 s )

L = 48 − 2 w 2 L = 48 − 2 w 2 or 24 − w 24 − w