Question

use the perimeter formula for a rectangle, $p = 2(ell + w)$ or $p = 2ell+2w$, to solve.

1. find $p$ when $ell = 71$ and $w = 33$.

$p = 2(71)+2(33)$
$p = 142 + 66$
$p = 208$ units

1. find $p$ when $ell = 24$ and $w = 4$.
2. find $w$ when $ell = 1$ and $p = 6$.
3. find $ell$ when $p = 24$ and $w = 4$.

use a formula to solve for the missing dimension.

Explanation:

Step1: Recall perimeter formula

The perimeter formula of a rectangle is $P = 2\ell+2w$.

Step2: Solve problem 16

Substitute $\ell = 24$ and $w = 4$ into the formula: $P=2\times24 + 2\times4$.
$P = 48+8$.
$P = 56$ units.

Step3: Solve problem 17

Given $P = 6$ and $\ell = 1$, substitute into $P = 2\ell+2w$: $6=2\times1 + 2w$.
$6 = 2+2w$.
Subtract 2 from both sides: $6 - 2=2w$, so $4 = 2w$.
Divide both sides by 2: $w = 2$ units.

Step4: Solve problem 18

Given $P = 24$ and $w = 4$, substitute into $P = 2\ell+2w$: $24=2\ell+2\times4$.
$24=2\ell + 8$.
Subtract 8 from both sides: $24 - 8=2\ell$, so $16 = 2\ell$.
Divide both sides by 2: $\ell = 8$ units.

Answer:

1. $P = 56$ units
2. $w = 2$ units
3. $\ell = 8$ units