Question

the length of a rectangle is 3 m longer than its width. if the perimeter of the rectangle is 58 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 \( l \) is \( w + 3 \) meters (since length is 3 m longer than width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 58 \) m. Substitute \( l = w + 3 \) into the formula:

$$ 58 = 2((w + 3) + w) $$

Step3: Simplify the equation

First, simplify inside the parentheses: \( (w + 3) + w = 2w + 3 \). Then the equation becomes:

$$ 58 = 2(2w + 3) $$

Divide both sides by 2:

$$ 29 = 2w + 3 $$

Step4: Solve for \( w \)

Subtract 3 from both sides:

$$ 29 - 3 = 2w $$

$$ 26 = 2w $$

Divide both sides by 2:

$$ w = 13 $$

Step5: Find the length

Since \( l = w + 3 \), substitute \( w = 13 \):

$$ l = 13 + 3 = 16 $$

Answer:

length: \( 16 \) m
width: \( 13 \) m