Question

the width of a rectangle measures (9v - 3) centimeters and its length measures (10v + 10) centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer: 20 + 6v, 14 + 38v, 12v + 40, 7 + 19v

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 $w=(9v - 3)$ and $l=(10v + 10)$. Then $P=2((10v + 10)+(9v - 3))$.

Step3: Simplify inside parentheses

$(10v + 10)+(9v - 3)=10v+9v + 10 - 3=19v + 7$.

Step4: Multiply by 2

$P = 2(19v + 7)=38v+14$.

Answer:

$14 + 38v$