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. length: cm width: cm

Explanation:

Step1: Define variables

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

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. Substituting the expressions for length and width:

$$ 68 = 2\times((x + 2) + x) $$

Step3: Simplify and solve for \( x \)

First, simplify the right - hand side:

$$ 68 = 2\times(2x + 2) $$

Divide both sides by 2:

$$ 34=2x + 2 $$

Subtract 2 from both sides:

$$ 32 = 2x $$

Divide both sides by 2:

$$ x = 16 $$

Step4: Find length and width

The width \( x = 16 \) cm. The length is \( x + 2=16 + 2 = 18 \) cm.

Answer:

length: \( 18 \) cm
width: \( 16 \) cm