Question

w.5 add polynomials to find perimeter 8as find the perimeter. simplify your answer. rectangle with top and bottom sides labeled p, left and right sides labeled 3p - 5

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length}+\text{width}) \). In this case, the length is \( p \) and the width is \( 3p - 5 \). So we can also calculate it by adding all four sides: \( P=p+(3p - 5)+p+(3p - 5) \).

Step2: Combine like terms

First, group the \( p \) terms and the constant terms:
\( p + 3p + p + 3p-5 - 5 \)
The sum of the \( p \) terms: \( p+3p + p+3p=(1 + 3+1 + 3)p = 8p \)
The sum of the constant terms: \( -5-5=-10 \)

Step3: Write the simplified perimeter

Combining these results, the perimeter is \( 8p-10 \).

Answer:

\( 8p - 10 \)