Question

the length of a rectangle is 5 m longer than its width. if the perimeter of the rectangle is 66 m, find its length and width. length: m width: m

Explanation:

Step1: Let the width be \( x \) meters.

Since the length is \( 5 \)m longer than the width, the length is \( x + 5 \) meters.

Step2: Use the perimeter formula \( P=2(l + w) \).

Given \( P = 66 \)m, substitute \( l=x + 5 \) and \( w=x \) into the formula:
\( 66=2((x + 5)+x) \)
Simplify the equation:
\( 66=2(2x + 5) \)
\( 66 = 4x+10 \)
Subtract \( 10 \) from both sides:
\( 4x=66 - 10 \)
\( 4x=56 \)
Divide both sides by \( 4 \):
\( x = 14 \)

Step3: Find the length.

Since \( x = 14 \) (width), the length \( l=x + 5=14 + 5=19 \)

Answer:

length: \( 19 \)m
width: \( 14 \)m