Question

the length of a rectangle is three times its width. if the perimeter of the rectangle is 40 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 \( l = 3w \) cm.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P=2(l + w) \). Substitute \( l = 3w \) and \( P = 40 \) into the formula:
\( 40=2(3w+w) \).
Simplify the right - hand side: \( 40 = 2\times4w\), so \( 40=8w \).

Step3: Solve for \( w \)

Divide both sides of the equation \( 40 = 8w \) by 8: \( w=\frac{40}{8}=5 \) cm.

Step4: Solve for \( l \)

Since \( l = 3w \), substitute \( w = 5 \) into the equation: \( l=3\times5 = 15 \) cm.

Answer:

length: \( 15 \) cm, width: \( 5 \) cm