Since the problem said he uses 160 feet of fence, you know that is the perimeter
P = 2l + 2w
You know that one of the dimensions is 50, so you can plug that into the equation
160 = 2 x 50 + 2w
160 = 100 + 2w
2w = 60
w = 30
The area is equal to l x w
50 x 30 = 1500 square feet