Question

the length of a rectangle is three times its width. if the perimeter of the rectangle is 48 cm, find its length and width.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) cm. Then the length \( l \) is \( 3w \) cm (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 \( P = 48 \) cm.

Step3: Substitute values into formula

Substitute \( l = 3w \) and \( P = 48 \) into the perimeter formula:
\[
48 = 2(3w + w)
\]

Step4: Simplify and solve for \( w \)

First, simplify the expression inside the parentheses: \( 3w + w = 4w \). So the equation becomes:
\[
48 = 2(4w)
\]
\[
48 = 8w
\]
Divide both sides by 8:
\[
w = \frac{48}{8} = 6
\]

Step5: Find the length

Since \( l = 3w \), substitute \( w = 6 \):
\[
l = 3 \times 6 = 18
\]

Answer:

The width of the rectangle is \( 6 \) cm and the length is \( 18 \) cm.