How to Solve Perimeter Problems Like a Pro: A Simple Step-by-Step Guide (With Example)

Understanding perimeter calculations is essential in geometry, whether you're measuring a garden, a room, or any enclosed space. Today, we’ll walk through a clear, practical example to help you master how to solve perimeter problems step by step.

Understanding the Context

Understanding the Perimeter Formula

The perimeter of a rectangle is calculated using the formula:

\[
\ ext{Perimeter} = 2 \ imes (\ ext{length} + \ ext{width})
\]

Given that one side (let’s say the width) is defined as \( w \), and the adjacent side is three times that width (\( 3w \)), we substitute into the formula:

Solved: Thinking 1. a) Solve the perimeter formula P = 2(l+w) 'w'' . b ...

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Solved: Thinking 1. a) Solve the perimeter formula P = 2(l+w) 'w'' . b ...
Solved a) The perimeter of a rectangle is P = 2L + 2W, where | Chegg.com
Solved = lw and the formula for perimeter Pis P = 21 + 2W. | Chegg.com
Solved Use the perimeter formula P=2l+2w to find the length, | Chegg.com
Solved Rule Perimeter =2( Length )+2( Width ) Or P=2L+2W | Chegg.com

Key Insights

\[
\ ext{Perimeter} = 2 \ imes (w + 3w)
\]

Step-by-Step Breakdown

  1. Add the dimensions inside the parentheses:
    \[
    w + 3w = 4w
    \]

  2. Multiply by 2 to find the full perimeter:
    \[
    2 \ imes 4w = 8w
    \]

  3. Set the perimeter equal to the given value:
    If the perimeter is 64 meters:
    \[
    8w = 64
    \]

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Final Thoughts

  1. Solve for \( w \):
    Divide both sides by 8:
    \[
    w = \frac{64}{8} = 8
    \]

So, the width \( w = 8 \) meters.

Finding the Full Dimensions

Since the width is 8 meters and the length is \( 3w \):
\[
\ ext{Length} = 3 \ imes 8 = 24 \ ext{ meters}
\]

This confirms our rectangle has dimensions 24 m × 8 m, with a perimeter of \( 2(24 + 8) = 64 \) meters — exactly matching the problem.

Why This Method Works

This approach applies to any rectangle where one dimension is a known multiple of the other. By using the perimeter formula and substituting variables, you can quickly solve for unknown sides every time.