Question

1. a rectangle has a length that is three feet more than twice its width.

(a) if the width of the rectangle is represented by the variable w, give an expression for the length of the rectangle in terms of w.
(b) what would the perimeter of this rectangle be if the width was 10 feet?

Explanation:

Step1: Find length expression

The length $l$ is three feet more than twice the width $w$. So $l = 2w+3$.

Step2: Recall perimeter formula

The perimeter $P$ of a rectangle is $P=2(l + w)$. Substitute $l = 2w + 3$ into the formula: $P=2((2w + 3)+w)=2(3w + 3)=6w+6$.

Step3: Calculate perimeter for $w = 10$

Substitute $w = 10$ into the perimeter formula $P=6w + 6$. So $P=6\times10+6=60 + 6=66$.

Answer:

(a) $l=2w + 3$
(b) 66 feet