Question

find the perimeter. simplify your answer. (diagram: rectangle with top and bottom sides labeled p, left and right sides labeled p-1)

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by the formula \( P = 2\times(\text{length} + \text{width}) \). In this case, the length is \( p \) and the width is \( p - 1 \).

Step2: Substitute the values into the formula

Substitute length \( = p \) and width \( = p - 1 \) into the formula:
\[
P = 2\times(p + (p - 1))
\]

Step3: Simplify the expression inside the parentheses

First, simplify \( p + (p - 1) \):
\[
p + p - 1 = 2p - 1
\]

Step4: Multiply by 2

Now multiply the simplified expression by 2:
\[
P = 2\times(2p - 1) = 4p - 2
\]

Answer:

\( 4p - 2 \)