Question

the length of a rectangle is four times its width. if the perimeter of the rectangle is 60 m, find its length and width. length: m width: m

Explanation:

Step1: Let the width be \( x \)

Let the width of the rectangle be \( x \) meters. Since the length is four times the width, the length is \( 4x \) meters.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is \( P = 2(l + w) \). Given \( P=60 \) m, substitute \( l = 4x \) and \( w = x \) into the formula: \( 60=2(4x + x) \).
Simplify the right - hand side: \( 60 = 2\times5x\), so \( 60 = 10x \).

Step3: Solve for \( x \)

Divide both sides of the equation \( 60 = 10x \) by 10: \( x=\frac{60}{10}=6 \).

Step4: Find the length

Since the length \( l = 4x \), substitute \( x = 6 \) into it. Then \( l=4\times6 = 24 \).

Answer:

length: \( 24\) m
width: \( 6\) m