Question

the width of a rectangle measures (10p - 9q) centimeters, and its length measures (7p + 8q) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
-2 + 34p 17p - 1
-9 + 16q + 34p -2q + 34p

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. Here, $l=(7p + 8q)$ and $w=(10p - 9q)$.

Step2: Substitute length and width

$P=2((7p + 8q)+(10p - 9q))$.

Step3: Simplify inside parentheses

$(7p + 8q)+(10p - 9q)=(7p+10p)+(8q - 9q)=17p - q$.

Step4: Multiply by 2

$P = 2(17p - q)=34p-2q$.

Answer:

$-2q + 34p$