Perimeter = 2(w + 3w) = 2(4w) = 8w = 64 → w = 64 / 8 = <<64 / 8 = 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 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:
\[\ ext{Perimeter} = 2 \ imes (w + 3w)\]
Step-by-Step Breakdown
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Add the dimensions inside the parentheses: \[ w + 3w = 4w \]
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Multiply by 2 to find the full perimeter: \[ 2 \ imes 4w = 8w \]
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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.
Final Answer:
\[\boxed{w = 8 \ ext{ meters}}\]
Use this step-by-step method to tackle similar perimeter puzzles with confidence — whether in school, home improvement projects, or practical applications!
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