Perimeter = 2(w + 3w) = 2(4w) = 8w = 64 → w = 64 / 8 = <<64 / 8 = 8>>8 meters - Coaching Toolbox
How to Solve Perimeter Problems Like a Pro: A Simple Step-by-Step Guide (With Example)
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:
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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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- 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.
