the volume of the box is l*w*h, or l*w*10, and also the volume is 360. so, 10lw=360, meaning l*w=36, so we are looking for whole number factors of 36.
length: 1 2 3 4 6 9 12 18 36width:36 18 12 9 6 4 3 2 1
there are a total of 9 possible ways to make the base of the box so your answer would be 9