36 ft
The area of a rectangle is the product of length and width. Here, you have the width being 2/3 the length. Put the given values into the area formula and solve.
A = L·W
864 ft² = L · (2/3·L)
1296 ft² = L² . . . . . . . multiply by 3/2
36 ft = L . . . . . . . . . . . take the square root
The length of Louis's basement is 36 feet.