1.8.4 Writing Equations Given Dimensions of Shapes

Algebra 11.8.4 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: $2 \cdot length + 2 \cdot width = 48$ .

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

10 centimeters

$2 L + 2 (10) = 48$

$2 L + 20 = 48$

$2 L + 20 - 20 = 48 - 20$

$2 L = 28$

$\frac{1}{2} (2 L) = \frac{1}{2} (28)$

$L = 14$

3.6 centimeters

$2 L + 2 (3.6) = 48$

$2 L + 7.2 = 48$

$2 L + 7.2 - 7.2 = 48 - 7.2$

$2 L = 40.8$

$\frac{1}{2} (2 L) = \frac{1}{2} (40.8)$

$L = 20.4$

$w$ centimeters

Compare your answer:

$2 L + 2 (w) = 48$

$2 L + 2 w = 48$

$2 L + 2 w - 2 w = 48 - 2 s$

$2 L = 48 - 2$

$\frac{1}{2} (2 L) = \frac{1}{2} (48 - 2 s)$

$L = \frac{48 - 2 w}{2}$ or $24 - w$

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