Question

the length of a rectangle is three times its width.
if the perimeter of the rectangle is 64 yd, find its length and width.
length: yd
width: yd

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) yd. Then the length \( l = 3w \) yd.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Given \( P = 64 \) yd. Substitute \( l = 3w \) into the formula: \( 64=2(3w + w) \).

Step3: Simplify the equation

First, simplify inside the parentheses: \( 3w+w = 4w \). So the equation becomes \( 64 = 2\times4w\), which simplifies to \( 64=8w \).

Step4: Solve for \( w \)

Divide both sides of the equation \( 64 = 8w \) by 8: \( w=\frac{64}{8}=8 \) yd.

Step5: Solve for \( l \)

Since \( l = 3w \), substitute \( w = 8 \) into the equation: \( l=3\times8 = 24 \) yd.

Answer:

length: \( 24 \) yd, width: \( 8 \) yd