Question

the length of a rectangle is five times its width. if the perimeter of the rectangle is 72 yd, find its length and width. length: \boxed{} yd width: \boxed{} yd

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) yards. Then the length \( l \) is \( 5w \) yards (since length is five times the width).

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 72 \) yd. Substitute \( l = 5w \) into the formula:

$$ 72 = 2(5w + w) $$

Step3: Simplify and solve for \( w \)

First, simplify the expression inside the parentheses: \( 5w + w = 6w \). So the equation becomes:

$$ 72 = 2(6w) $$

$$ 72 = 12w $$

Divide both sides by 12:

$$ w = \frac{72}{12} = 6 $$

Step4: Find the length

Since \( l = 5w \), substitute \( w = 6 \):

$$ l = 5 \times 6 = 30 $$

Answer:

length: \( 30 \) yd
width: \( 6 \) yd