Question

the width of a rectangle measures (3u - 4v) centimeters, and its length measures (10u + 2v) centimeters. which expression represents the perimeter, in centimeters, of the rectangle? answer -4 + 26u + 4v 26u - 4v 13u - 2 26u - 4

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is length and $w$ is width. Here, $l=(10u + 2v)$ and $w=(3u - 4v)$.

Step2: Substitute values into formula

$P=2((10u + 2v)+(3u - 4v))$.

Step3: Simplify inside parentheses

First, combine like - terms inside the parentheses: $(10u+3u)+(2v - 4v)=13u-2v$. So, $P = 2(13u - 2v)$.

Step4: Distribute the 2

Using the distributive property $a(b + c)=ab+ac$, we have $P=2\times13u-2\times2v = 26u-4v$.

Answer:

$26u - 4v$