Let the three sides of the box be P, Q and R.
Now we know the area of rectangle is l* b.
P * Q = 240
P * R = 300
Q * R = 180
Let us multiply these three equations:
(P*Q) (P*R) (R*S) = 240 * 300 * 180
P^2 * Q ^2 * R^2 = 12960000
(P*Q*R)^2 = 12960000
P*Q*R = 3600
Now we know that P*Q = 240
Thus R = 3600/240 = 15.
Similarly putting and solving for other variables, we get
P = 20 units
Q = 12 units
R = 15 units