Since the triangle is a right isosceles triangle and each leg measures x, its area is given by:
[tex]A=\frac{1}{2}x^2[/tex]
Now, let's use the given area and solve it for x:
[tex]\begin{gathered} 4232=\frac{1}{2}x^2\\ \\ x^2=8464\\ \\ x=92\text{ ft} \end{gathered}[/tex]
Since the "path" already has fence, the amount of fence needed is 2x:
[tex]2x=2\cdot92=184\text{ ft}[/tex]
