Question

the length of a rectangle is 3 in longer than its width. if the perimeter of the rectangle is 66 in, find its length and width. your answer length: 3 in width: 22 in

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) inches. Then the length \( l \) is \( w + 3 \) inches.

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 66 \), so substitute \( l = w + 3 \) into the formula:

$$ 66 = 2((w + 3) + w) $$

Step3: Simplify the equation

First, simplify the expression inside the parentheses:

$$ 66 = 2(2w + 3) $$

Then divide both sides by 2:

$$ 33 = 2w + 3 $$

Subtract 3 from both sides:

$$ 30 = 2w $$

Divide both sides by 2:

$$ w = 15 $$

Step4: Find the length

Since \( l = w + 3 \), substitute \( w = 15 \):

$$ l = 15 + 3 = 18 $$

Answer:

length: 18 in
width: 15 in