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

In a rectangular parallelepiped, the length is 3 times its width and 2 times its height. Find the measurements of a rectangular parallelepiped if its surface area is 864 cm2.

Let’s take for x – the width of the parallelepiped, then:

3 * x – long;

2 * 3 * x – height.

We get the equation:

2 * (6x * x + 6x * 3x + x * 3x) = 864;

54x = 864;

x = 864: 54 = 16 cm.

Then the length is equal to:

3 * 16 = 48 cm;

Height:

48 * 2 = 96 cm.

Answer: the dimensions of the parallelepiped are 16, 48 and 96 cm.