Question

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

Explanation:

Step1: Define variables for width/length

Let width = $w$ in. Then length = $w+4$ in.

Step2: Use perimeter formula

Perimeter of rectangle: $P=2(\text{length}+\text{width})$
Substitute values: $52=2((w+4)+w)$

Step3: Simplify and solve for $w$

First simplify inside parentheses:
$52=2(2w+4)$
Divide both sides by 2:
$26=2w+4$
Subtract 4 from both sides:
$22=2w$
Divide by 2:
$w=11$

Step4: Calculate length

Length = $w+4=11+4=15$

Answer:

length: 15 in
width: 11 in