Question

the width of a rectangle measures $(8n + 7p)$ centimeters, and its length measures $(2n + 8p)$ centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
$16p + 20n+7$
$20n + 30p$
$20n + 30$
$15 + 10n$
submit answer

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step2: Substitute length and width

Here, $w=(8n + 7p)$ and $l=(2n + 8p)$. So $P = 2((2n + 8p)+(8n + 7p))$.

Step3: Simplify inside parentheses

$(2n + 8p)+(8n + 7p)=2n+8n + 8p+7p=10n + 15p$.

Step4: Multiply by 2

$P = 2(10n + 15p)=20n+30p$.

Answer:

$20n + 30p$