Question

find the perimeter. simplify your answer.
$w - 4$
$9w - 2$
$w - 4$
$9w - 2$

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, the length is \( 9w - 2 \) and the width is \( w - 4 \). So we can also calculate the perimeter by adding all four sides: \( P=(9w - 2)+(w - 4)+(9w - 2)+(w - 4) \).

Step2: Combine like terms

First, group the \( w \) terms and the constant terms:
\( P=(9w+w + 9w+w)+(-2-4 - 2-4) \)
Calculate the coefficients of \( w \): \( 9 + 1+9 + 1 = 20 \)
Calculate the constant terms: \( -2-4-2 - 4=-12 \)
So \( P = 20w-12 \)

Answer:

\( 20w - 12 \)