Alex is building a rectangular fence around his yard. the total perimeter of the fence is 68 feet and the area of the yard is 250 square feet. based on this information, what are the dimensions of the fence

Let
x-------------> length of the fence
y-------------> width of the fence

we know that
Area of rectangle=x*y
perimeter of rectangle=2x+2y
A=250 ft²
P=68 ft

then
250=x*y-----------> x=250/y  equation 1
68=2x+2y-----------> equation 2

using a graph tool---------> to resolve the system of equations
see the attached figure

the solution is the point 1 (10.755,23.245)  and the point 2 (23.245,10.755)

for the point 1
x=10.755 ft
y=23.245 ft

for the point 2
x=23.245 ft
y=10.755 ft

the answer is
the dimensions of the fence are
23.245 ft x 10.755 ft 
or
10.755 ft x 23.245 ft