Answer:
29 ft x 58 ft
Step-by-step explanation:
Let x be the length of each side perpendicular to the wall, and y be the length of the side parallel to the wall.
The amount of wire available is:
[tex]116 = 2x+y\\y=116-2x[/tex]
The area of the region is:
[tex]A=xy=x(116-2x)\\A(x)=116x-2x^2[/tex]
The value of 'x' for which the derivate of the area function is zero will yield the maximum area:
[tex]A(x)=116x-2x^2\\A'(x) = 116-4x=0\\x=29\ ft[/tex]
The value of y is:
[tex]y=116-2*29\\y=58\ ft[/tex]
The dimensions of the region with the largest area are 29 ft x 58 ft.
