Perimeter = 2(w + 3w) = 2(4w) = 8w = 64 → w = 64 / 8 = 8 meters

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 ...

Image Gallery

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

Add the dimensions inside the parentheses:
\[
w + 3w = 4w
\]
Multiply by 2 to find the full perimeter:
\[
2 \ imes 4w = 8w
\]
Set the perimeter equal to the given value:
If the perimeter is 64 meters:
\[
8w = 64
\]

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Final Thoughts

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.