The plans for a shed call for a rectangular floor with a perimeter of 198 ft. The length is The two times the width. How do you find the length and width?

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Answer 1 · 2017-01-07T21:21:03

See full explanation for how to find the length and width below in the explanation:

The formula for a perimeter is:

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

Where
$p$ $p$ is the perimeter
$w$ $w$ is the width
$l$ $l$ is the length.

And, we know from the problem:

$l = 2 w$ $l = 2w$

We can then substitute $2 w$ $2w$ for $l$ $l$ in the equation for the perimeter to give:

$p = 2 w + (2 \times 2 w)$ $p = 2w + (2 xx 2w)$

$p = 2 w + 4 w$ $p = 2w + 4w$

$p = 6 w$ $p = 6w$

We also know the perimeter will be 198 ft so we can substitute this for $p$ $p$ and solve for $w$ $w$ , the width:

$198 = 6 w$ $198 = 6w$

$\frac{198}{6} = \frac{6 w}{6}$ $198/color(red)(6) = (6w)/color(red)(6)$

$33 = w$ $33 = w$ or $w = 33$ $w = 33$

And because we know:

$l = 2 w$ $l = 2w$ we can substitute $33$ $33$ for $w$ $w$ and solve for $l$ $l$ :

$l = 2 \times 33$ $l = 2 xx 33$

$l = 66$ $l = 66$

The length of the floor will be 66 ft and the width will be 33 ft.