Question #e627c

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Question #e627c

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Answer 1 · 2017-11-03T02:00:41

See below.

Explanation:

Based on the given information, we can write the following equations:

$p = w + 12$ $p=w+12$

$p = 7 w$ $p=7w$

$p = 2 w + 2 l$ $p=2w+2l$

where $p$ $p$ is the perimeter, $l$ $l$ is the length, and $w$ $w$ is the width.

Our goal is to find $l$ $l$ in the third equation. But before we do this, we will need to solve for $p$ $p$ and $w$ $w$ in the first and second equations listed above (I am using the substitution method):

$p = w + 12$ $p=w+12$ and $p = 7 w$ $p=7w$

$(p) = w + 12$ $(color(blue)(p))=w+12$

$(7 w) = w + 12$ $color(blue)((7w))=w+12$

$6 w = 12$ $6w=12$

$w = 2$ $color(red)(w=2)$

Now, we will use the width, $w = 2$ $w=2$ , to find the perimeter (it doesn't matter whether you use equation $1$ $1$ or $2$ $2$ here):

$p = 7 w$ $p=7color(blue)(w)$

$p = 7 (2)$ $p=7color(blue)((2))$

$p = 14$ $color(red)(p=14)$

Now, we know both of the values of $p$ $p$ and $w$ $w$ , and we are ready to use them to find $l$ $l$ using the third equation:

$p = 2 w + 2 l$ $color(green)(p)=2color(blue)(w)+2l$

$(14) = 2 (2) + 2 l$ $color(green)((14))=2(color(blue)(2))+2l$

$14 = 4 + 2 l$ $14=4+2l$

$10 = 2 l$ $10=2l$

$l = 5$ $color(red)(l=5)$

Therefore, the length of your rectangle is $5 inches$ $color(green)(5 " inches"$ .

I hope that helps!

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Question #e627c

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