In a rectangular parallelepiped, the length is 3 times its width and 2 times

In a rectangular parallelepiped, the length is 3 times its width and 2 times its height. Find the dimensions of a parallelepiped if its surface area is 864 cm ^ 2.

Let’s solve the problem using the equation.
Let the length of a rectangular paralelepipid be xcm, then its width is (x / 3) cm, and its height is 2x cm.
The area of the parallelepiped is 2 (ab + bc + ac), where a is the length, b is the width, and c is the height.
That is, the area is 2 (x (x / 3) + x * 2x + 2x (x / 3). According to the conditions of the problem, the area is 864
2 (x (x / 3) + x * 2x + 2x (x / 3) = 864
2 ((x ^ 2) / 3 + 2x ^ 2 + (2/3) x ^ 2) = 864
(x ^ 2) / 3 + 2x ^ 2 + (2/3) x ^ 2 = 432
x ^ 2 + 6x ^ 2 + 2x ^ 2 = 1296
9x ^ 2 = 1296
x ^ 2 = 144
x + 12
This means that the length of the rectangular parallelepiped is 12 cm, the width is 12/3 = 4 cm, and the height is 2 * 12 = 24 cm.
Answer: 12 cm, 4 cm, 24 cm