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:

( \bigcirc ) a. ( \frac{p}{5} )

( \bigcirc ) b. ( \frac{p}{4} )

( \bigcirc ) c. ( \frac{p}{2} )

( \bigcirc ) d. ( \frac{p-2}{2} )

( \bigcirc ) e. ( \frac{p-4}{4} )

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \). Then the length \( l = w + 2 \).

Step2: Recall perimeter formula

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

Step3: Substitute length into formula

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

Step4: Simplify the equation

Simplify the right - hand side: \( P = 2(2w + 2)=4w + 4 \).

Step5: Solve for \( w \)

First, subtract 4 from both sides: \( P - 4=4w \). Then divide both sides by 4: \( w=\frac{P - 4}{4} \).

Answer:

E. \(\frac{P - 4}{4}\)