Questions: The length of a rectangle is 5 m longer than its width. If the perimeter of the rectangle is 58 m, find its length and width.

Find the length and width of the rectangle.

Define variables.

Let the width of the rectangle be \( w \) meters. Then, the length is \( w + 5 \) meters.

Write the perimeter formula.

The perimeter \( P \) of a rectangle is given by:
\[ P = 2(\text{length} + \text{width}) \]
Substitute the known values:
\[ 58 = 2((w + 5) + w) \]

Simplify the equation.

Combine like terms inside the parentheses:
\[ 58 = 2(2w + 5) \]
Multiply out the right side:
\[ 58 = 4w + 10 \]

Solve for \( w \).

Subtract 10 from both sides:
\[ 58 - 10 = 4w \]
\[ 48 = 4w \]
Divide both sides by 4:
\[ w = 12 \]

Find the length.

The length is \( w + 5 \):
\[ \text{length} = 12 + 5 = 17 \]

The width is \( \boxed{12 \, \text{m}} \), and the length is \( \boxed{17 \, \text{m}} \).

The width is \( \boxed{12 \, \text{m}} \), and the length is \( \boxed{17 \, \text{m}} \).