Question

1. the length of a rectangle is nine more than twice the width. write a simplified expression that could be used to find the perimeter of the rectangle.

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = 2w + 9$.

Step2: Recall perimeter formula

The perimeter $P$ of a rectangle is given by $P=2(l + w)$.

Step3: Substitute length expression

Substitute $l = 2w + 9$ into the perimeter formula: $P = 2((2w + 9)+w)$.

Step4: Simplify the expression

First, simplify the expression inside the parentheses: $(2w + 9)+w=3w + 9$. Then $P = 2(3w + 9)$. Distribute the 2: $P=6w + 18$.

Answer:

$6w + 18$