Solution:
Given that John wishes to build a square fence with an area of 121 square yards, as shown below:
The area of a square is expressed as
[tex]\begin{gathered} Area\text{ of square = L}^2 \\ where \\ L\Rightarrow length\text{ of a side of the square} \end{gathered}[/tex]Given that the area of the square fence is 121 square yards, this implies that
[tex]\begin{gathered} 121=L^2 \\ take\text{ the square root of both sides,} \\ \sqrt{121\text{ }}\text{ =}\sqrt{L^2} \\ \sqrt{11\times11}\text{ =}\sqrt{L\times L} \\ \Rightarrow L=11\text{ yards} \end{gathered}[/tex]The perimeter of a square is expressed as
[tex]\begin{gathered} Perimeter\text{ of square = 4}\times L \\ where \\ L\Rightarrow length\text{ of a side of the square} \end{gathered}[/tex]Thus, the perimeter of the fence is evaluated by substituting the value of 11 for L into the perimeter formula.
[tex]\begin{gathered} Perimeter\text{ of fence = 4}\times11 \\ \Rightarrow Perimeter\text{ of fence = 44 yards} \end{gathered}[/tex]Hence, the perimeter of the fence is 44 yards.
