What is the length and width of a square 40 acre parcel?

First of all, if it's square, then the length and width are equal.

As a rule, you can't tell the dimensions from the area. But since you've specified that the

parcel is square, that makes all the difference. There's only one square with that area.

1 acre = 43,560 square feet

40 acres = (40 x 43,560) = 1,742,400 square feet

The square is 1,320-ft = 1/4 mile on each side.

==============================

An easier solution:

1 square mile = 640 acres

40 acres = 40/640 = 1/16th square mile

sqrt(1/16th) = 1/4 mile