Question 848163
170 = 2L + 2W

2800 = L*W

2800/W = L

170 = 2*(2800/W) + 2W 

170 = 5600/W + 2W

170W/W = 5600/W  + 2W^2/W

W isn't 0, so we can ignore the denominator.

170W = 5600 + 2W^2

2W^2 - 170W +5600

2(W^2 - 85W + 2800)

This has no real solution. You can compute this by taking b^2 - 4ac, which is clearly less than 0.

Another thing we can notice that confirms this is say our rectangle has the same length and width. This maximizes our area (also known as a square). Then each side would have 42.5, and so 42.5^2 = 1806.25 which is the maximum area possible. This is not necessary to know, but it confirms that there is no real solution.