Question

the length of a rectangle is three times its width. if the perimeter of the rectangle is 48 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 \( 3w \) yards (since length is three times width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 48 \) yd, so substitute \( l = 3w \) into the formula:
\( 48 = 2(3w + w) \)
Simplify inside the parentheses: \( 3w + w = 4w \), so \( 48 = 2(4w) = 8w \).

Step3: Solve for width

Divide both sides by 8: \( w=\frac{48}{8}=6 \) yd.

Step4: Solve for length

Since \( l = 3w \), substitute \( w = 6 \): \( l = 3\times6 = 18 \) yd.

Answer:

length: \( 18 \) yd
width: \( 6 \) yd