Question

1. simplify an expression for the perimeter of the rectangle. perimeter: rectangle with top/bottom sides labeled 3w, left/right sides labeled 5w - 2

Explanation:

Step1: Recall rectangle perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, length is \( 5w - 2 \) and width is \( 3w \).

Step2: Substitute into the formula

\( P = 2\times((5w - 2) + 3w) \)

Step3: Simplify inside the parentheses

\( (5w - 2) + 3w = 5w + 3w - 2 = 8w - 2 \)

Step4: Multiply by 2

\( P = 2\times(8w - 2) = 16w - 4 \)

Answer:

\( 16w - 4 \)