Question

the width of a rectangle measures (9b - 8c) centimeters, and its length measures (7b + 6c) centimeters. which expression represents the perimeter, in centimeters, of the rectangle?
answer
32b - 4c
-4 + 32b
12c - 8 + 32b
16b - 2
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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

Given $w=9b - 8c$ and $l = 7b+6c$. Then $P=2((7b + 6c)+(9b - 8c))$.

Step3: Simplify inside the parentheses

$(7b + 6c)+(9b - 8c)=7b+9b+6c - 8c=16b - 2c$.

Step4: Multiply by 2

$P = 2(16b - 2c)=32b-4c$.

Answer:

$32b - 4c$