Question

the length of a rectangle is 2 inches more than its width. if p represents the perimeter of the rectangle, then its width is:
a. $\frac{p}{5}$
b. $\frac{p}{4}$
c. $\frac{p}{2}$
d. $\frac{p - 2}{2}$
e. $\frac{p - 4}{4}$

Explanation:

Step1: Define variables

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

Step2: Recall perimeter formula

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

Step3: Substitute length into formula

Substitute $l = w + 2$ into $P = 2(l + w)$, we get $P=2((w + 2)+w)=2(2w + 2)=4w+4$.

Step4: Solve for width

First, rewrite the equation $P = 4w+4$ as $4w=P - 4$. Then $w=\frac{P - 4}{4}$.

Answer:

E. $\frac{P - 4}{4}$