What is the volume of a rectangular parallelepiped, the areas of three faces of which are equal to 12 cm, 15 cm, and 20 cm?

Let us denote the lengths of the sides of the parallelepiped as A, B and C.

Then:

A * B = 12 cm2.

A * C = 20 cm2.

B * C = 15 cm2.

Let’s solve the system of three equations by the substitution method.

A = 12 / B.

C = 15 / V.

Then 12 / B) * (15 / B) = 20.

B2 = (12 * 15) / 20 = 9.

B = 3 cm.

Then A = 12/3 = 4 cm.

C = 15/3 = 5 cm.

Let’s define the volume of the parallelepiped.

V = A * B * C = 4 * 3 * 5 = 60 cm3.

Answer: The volume of a parallelepiped is 60 cm3.