Question

the length of a rectangle is 4 ft longer than its width. if the perimeter of the rectangle is 52 ft, find its length and width.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( x \) ft. Then the length is \( x + 4 \) ft (since length is 4 ft longer than width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(\text{length} + \text{width}) \). We know \( P = 52 \) ft, so substitute the expressions for length and width:
\[
52 = 2((x + 4) + x)
\]

Step3: Simplify and solve for \( x \)

First, simplify the equation inside the parentheses:
\[
52 = 2(2x + 4)
\]
Divide both sides by 2:
\[
26 = 2x + 4
\]
Subtract 4 from both sides:
\[
22 = 2x
\]
Divide both sides by 2:
\[
x = 11
\]

Step4: Find length

The length is \( x + 4 \), so substitute \( x = 11 \):
\[
\text{length} = 11 + 4 = 15
\]

Answer:

length: 15 ft
width: 11 ft