Question

the length of a rectangle is four times its width. if the perimeter of the rectangle is 80 m, find its length and width.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) meters. Then the length \( l \) is \( 4w \) meters (since length is four times the width).

Step2: Use the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by the formula \( P = 2(l + w) \). We know the perimeter is 80 m, so we substitute \( l = 4w \) and \( P = 80 \) into the formula:
\[
80 = 2(4w + w)
\]

Step3: Simplify and solve for \( w \)

First, simplify the expression inside the parentheses:
\[
80 = 2(5w)
\]
\[
80 = 10w
\]
Then, divide both sides by 10 to solve for \( w \):
\[
w = \frac{80}{10} = 8
\]

Step4: Find the length

Since the length \( l = 4w \), substitute \( w = 8 \):
\[
l = 4 \times 8 = 32
\]

Answer:

The width of the rectangle is \( 8 \) m and the length is \( 32 \) m.