Question

the length of a rectangle is 4 yd longer than its width. if the perimeter of the rectangle is 64 yd, find its length and width.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) yards. Then the length \( l = w + 4 \) yards.

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 64 \) yards. Substitute \( l = w + 4 \) into the formula:

$$ 64 = 2((w + 4) + w) $$

Step3: Simplify the equation

First, simplify the inside of the parentheses: \( (w + 4) + w = 2w + 4 \). Then the equation becomes:

$$ 64 = 2(2w + 4) $$

Divide both sides by 2:

$$ 32 = 2w + 4 $$

Subtract 4 from both sides:

$$ 28 = 2w $$

Divide both sides by 2:

$$ w = 14 $$

Step4: Find the length

Since \( l = w + 4 \), substitute \( w = 14 \):

$$ l = 14 + 4 = 18 $$

Answer:

length: \( 18 \) yd, width: \( 14 \) yd