11. simplify an expression for the perimeter of the rectangle.
3w
5w - 2
perimeter:

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the perimeter of a rectangle
The formula for the perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l=5w - 2$ and $w = 3w$.
## Step2: Substitute the values of length and width into the formula
$$
\begin{align*}
P&=2((5w - 2)+3w)\
&=2(5w+3w - 2)
\end{align*}
$$
## Step3: Simplify the expression inside the parentheses
$$
\begin{align*}
P&=2(8w - 2)
\end{align*}
$$
## Step4: Use the distributive property $a(b + c)=ab+ac$
$$
\begin{align*}
P&=2\times8w-2\times2\
&=16w - 4
\end{align*}
$$

# Answer:
$16w - 4$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the perimeter of a rectangle

Step2: Substitute the values of length and width into the formula

Step3: Simplify the expression inside the parentheses

Step4: Use the distributive property \(a(b + c)=ab+ac\)

Answer: