The width of the rectangular parallelepiped is 60% of the length, and the height is 120% of the length.

The width of the rectangular parallelepiped is 60% of the length, and the height is 120% of the length. Find the volume of this rectangular parallelepiped if the sum of the lengths of its edges is 56 dm.

It is not difficult to determine the number of edges of a parallelepiped – 12. That is, each parallelepiped has 4 lengths, 4 widths and 4 heights.

Let x be the length of the parallelepiped, y the width, and z the height, respectively.

We get:

4 * x + 4 * y + 4 * z = 56;

4 * (x + y + z) = 56;

x + y + z = 14.

It is known that the width is 60% of the length:

y = 0.6 * x;

It is also known that the height is 120% of the length:

z = 1.2 * x;

Substitute the resulting expressions for width and height and solve the equation:

x + 0.6 * x + 1.2 * x = 14;

2.8 * x = 14;

x = 5.

The length of the parallelepiped is 5 dm, the width is 3 dm, and the height is 6 dm.