Question

the length of a rectangle is 2 cm longer than its width. if the perimeter of the rectangle is 68 cm, find its length and width.

Explanation:

Step1: Define variables

Let the width of the rectangle be \( x \) cm. Then the length is \( x + 2 \) cm.

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). We know \( P = 68 \) cm, so:
\[
2\times((x + 2) + x) = 68
\]

Step3: Simplify the equation

First, simplify inside the parentheses: \( (x + 2) + x = 2x + 2 \). Then the equation becomes:
\[
2\times(2x + 2) = 68
\]
Divide both sides by 2:
\[
2x + 2 = 34
\]
Subtract 2 from both sides:
\[
2x = 32
\]
Divide both sides by 2:
\[
x = 16
\]

Step4: Find length and width

Width \( x = 16 \) cm. Length \( x + 2 = 16 + 2 = 18 \) cm.

Answer:

Width is \( 16 \) cm, Length is \( 18 \) cm.