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SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the formula for finding the perimeter of the fence
[tex]\begin{gathered} P=2L+2W \\ \text{where L is the length and W is the Width} \end{gathered}[/tex]STEP 2: Write the dimensions of the Fence
[tex]\begin{gathered} \text{The perimeter is 40m} \\ \text{Therefore,} \\ 2L+2W=40 \\ \text{ Making W the subject of the formula,} \\ 2W=40-2L \\ W=\frac{40-2L}{2} \\ W=20-L \\ \\ The\text{ length and the Width of the fence will be:} \\ L\text{ and 20-L} \end{gathered}[/tex]Hence, the width will result in the greatest possible area of the dog pen is:
[tex]20-L[/tex]STEP 3: Calculate the greatest possible area of the dog pen
[tex]\begin{gathered} \text{Area}=\text{Length}\times width \\ \text{Area}=L\times(20-L) \\ \text{Area}=20L-L^2 \end{gathered}[/tex]STEP 4: Calculate the length will result in the greatest possible area of the dog pen
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