Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 1 - Expressions, Equations, and Inequalities - 1-4 Solving Equations - Practice and Problem-Solving Exercises - Page 30: 28


$w=4.5cm$ $l=7.5cm$

Work Step by Step

$P=2l+2w$ where $l$ = length and $w$ = width The length of the rectangle is 3 cm greater than its width. Thus, $l=3+w$ The perimeter of the rectangle is $24$ Substitute these values into the original equation and solve for $w$. $24=2l+2w \\24=2(3+w)+2w \\24=6+2w+2w \\24=6+4w \\24-6=4w \\18=4w \\\frac{18}{4}=\frac{4w}{4} \\4.5=w$ The width is $4.5$ cm. Substitute $w$ into the equation for $l$: $l=3+w \\l=3+4.5 \\7.5=l$ The length is $7.5$ cm. To confirm that this is indeed correct, substitute the values of $l$ and $w$ into $P$. $P=2(7.5)+2(4.5)$ $P=15+9$ $P=24cm$
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