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: (square) yd
width: (square) yd

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) yards. Then the length \( l = 3w \) yards (since length is three times the width).

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 48 \) yards. Substitute \( l = 3w \) into the formula:

$$ 48 = 2(3w + w) $$

Step3: Simplify and solve for \( w \)

Simplify the right - hand side: \( 48 = 2(4w)=8w \). Then, divide both sides by 8: \( w=\frac{48}{8} = 6 \) yards.

Step4: Find the length

Since \( l = 3w \), substitute \( w = 6 \) into this equation: \( l=3\times6 = 18 \) yards.

Answer:

length: 18 yd
width: 6 yd