Question

the length of a rectangle is 6 cm longer than its width. if the perimeter of the rectangle is 72 cm, find its length and width. length: \boxed{} cm width: \boxed{} cm

Explanation:

Step1: Define variables

Let the width of the rectangle be \( x \) cm. Then the length is \( x + 6 \) cm (since length is 6 cm longer than width).

Step2: Recall perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Substituting the known values, we have \( 72 = 2\times((x + 6) + x) \).

Step3: Simplify the equation

First, simplify the inside of the parentheses: \( (x + 6) + x = 2x + 6 \). Then the equation becomes \( 72 = 2\times(2x + 6) \). Distribute the 2: \( 72 = 4x + 12 \).

Step4: Solve for x

Subtract 12 from both sides: \( 72 - 12 = 4x \), so \( 60 = 4x \). Divide both sides by 4: \( x = \frac{60}{4} = 15 \). So the width is 15 cm.

Step5: Find the length

The length is \( x + 6 = 15 + 6 = 21 \) cm.

Answer:

length: 21 cm
width: 15 cm