Question

the length of a rectangle is 6 m longer than its width. if the perimeter of the rectangle is 68 m, find its length and width. length: m width: m

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) meters. Then the length \( l=w + 6 \) meters.

Step2: Use the perimeter formula

The perimeter formula for a rectangle is \( P = 2(l + w) \). Given \( P=68 \) m, substitute \( l=w + 6 \) into the formula:
\( 68=2((w + 6)+w) \)
Simplify the equation:
\( 68=2(2w + 6) \)
\( 68 = 4w+12 \)

Step3: Solve for \( w \)

Subtract 12 from both sides:
\( 68-12=4w \)
\( 56 = 4w \)
Divide both sides by 4:
\( w=\frac{56}{4}=14 \)

Step4: Solve for \( l \)

Since \( l=w + 6 \), substitute \( w = 14 \):
\( l=14 + 6=20 \)

Answer:

length: \( 20 \) m, width: \( 14 \) m