Let the sides of the box be x, y and z.
We have:
xy = 30 --- (1)
xz = 70 --- (2)
yz = 84 --- (3)
From (1), we have:
x = 30 / y --- (4)
Substituting (4) into (2), we will get:
(30 / y)z = 70
z = 70y / 30
z = 7y / 3 --- (5)
Substituting (5) into (3), we will get:
y(7y / 3) = 84
7y^2 / 3 = 84
7y^2 = 252
y^2 = 252 / 7
y^2 = 36
y = sqrt(36)
y = 6
Substituting y = 6 into (5), we have:
z = 7(6) / 3
z = 7 * 2
z = 14
Substituting y = 6 into (4), we have:
x = 30 / 6
x = 5
Volume of box
= side * side * side
= x * y * z
= 5 * 6 * 14
= 420 units^3