Finding Dimensions of a Garden

Video Explanation

Question

Half the perimeter of a garden is 36 m. The length is 4 m more than the width. Find the dimensions of the garden.

Solution

Step 1: Let Variables

Let length = \(x\) m

Let width = \(y\) m

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Step 2: Use Perimeter Concept

Half perimeter = \(x + y = 36 \quad (1)\)

Given:

\[ x = y + 4 \quad (2) \]

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Step 3: Solve Linear Equations

Substitute (2) into (1):

\[ (y + 4) + y = 36 \]

\[ 2y + 4 = 36 \]

\[ 2y = 32 \Rightarrow y = 16 \]

Then:

\[ x = 16 + 4 = 20 \]

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Step 4: Final Answer

\[ \text{Length} = 20 \text{ m}, \quad \text{Width} = 16 \text{ m} \]

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Verification

Half perimeter = \(20 + 16 = 36\) ✔