The sum of the lengths of the edges emerging from one vertex of the rectangular parallelepiped is 40cm

The sum of the lengths of the edges emerging from one vertex of the rectangular parallelepiped is 40cm. Its height is h cm, its width is 2 times greater, and its length is 5 times its height. Calculate the volume of the rectangular parallelepiped.

From one vertex of a rectangular parallelepiped there are 3 different-sized edges corresponding to the height, width and length of this parallelepiped. If we take the height of the parallelepiped as 1 part (measure) equal to h, then the ratio of the lengths of the remaining edges can be written as 1: 2: 5 or:

h + 2 * h + 5 * h;

It is known that the sum of three edges is 40 cm, which means:

h + 2 * h + 5 * h = 40;

8 * h = 40;

h = 40: 8;

h = 5;

5 * h = 5 * 5 = 25;

2 * h = 2 * 5 = 10;

Consequently:

The parallelepiped is 5 cm high, 25 cm long and 10 cm wide.