Question

1. the length of a rectangle is 7 inches more than its width. if the perimeter of the rectangle is 66 inches, find its dimensions.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) inches. Then the length \( l \) is \( w + 7 \) inches.

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 66 \), so substitute \( l = w + 7 \) into the formula:
\( 66 = 2((w + 7) + w) \)

Step3: Simplify the equation

First, simplify inside the parentheses: \( (w + 7) + w = 2w + 7 \)
Then the equation becomes \( 66 = 2(2w + 7) \)
Divide both sides by 2: \( 33 = 2w + 7 \)

Step4: Solve for \( w \)

Subtract 7 from both sides: \( 33 - 7 = 2w \)
\( 26 = 2w \)
Divide both sides by 2: \( w = 13 \)

Step5: Find the length

Since \( l = w + 7 \), substitute \( w = 13 \): \( l = 13 + 7 = 20 \)

Answer:

The width of the rectangle is 13 inches and the length is 20 inches.