Question

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; 12c - 8 + 32b; -4 + 32b; 16b - 2

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, $l=(7b + 6c)$ and $w=(9b-8c)$.

Step2: Substitute values into formula

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

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:

$32b - 4c$