Question

the length of a rectangle is four times its width. if the perimeter of the rectangle is 100 cm, find its length and width. length: cm width: cm

Explanation:

Step1: Set up variables

Let the width of the rectangle be \( w \) cm. Then the length \( l = 4w \) cm.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 4w \) and \( P = 100 \) into the formula:
\( 100=2(4w + w) \)
Simplify the right - hand side: \( 100=2\times5w \), so \( 100 = 10w \).

Step3: Solve for \( w \)

Divide both sides of the equation \( 100 = 10w \) by 10: \( w=\frac{100}{10}=10 \) cm.

Step4: Solve for \( l \)

Since \( l = 4w \), substitute \( w = 10 \) into the equation: \( l=4\times10 = 40 \) cm.

Answer:

length: \( 40 \) cm, width: \( 10 \) cm