Question

the length of a rectangle is twice its width. if the perimeter of the rectangle is 54 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 \( l = 2w \) cm. The formula for the perimeter of a rectangle is \( P=2(l + w) \).

Step2: Substitute into the perimeter formula

Substitute \( l = 2w \) and \( P = 54 \) into \( P=2(l + w) \). We get \( 54=2(2w+w) \).
Simplify the right - hand side: \( 54 = 2\times3w\), so \( 54=6w \).

Step3: Solve for \( w \)

Divide both sides of the equation \( 54 = 6w \) by 6. \( w=\frac{54}{6}=9 \) cm.

Step4: Solve for \( l \)

Since \( l = 2w \), substitute \( w = 9 \). Then \( l=2\times9 = 18 \) cm.

Answer:

length: \( 18 \) cm, width: \( 9 \) cm