The sum of the lengths of the edges of the rectangular parallelepiped ABCDA1B1C1D1 is 80 cm.

The sum of the lengths of the edges of the rectangular parallelepiped ABCDA1B1C1D1 is 80 cm. Find the lengths of its edges if one of its dimensions is 3 cm more than the second and 20 cm less than the third.

Let’s denote one of the edges of the rectangular parallelepiped by x cm.

According to the condition of the problem, one of the measurements is 3 cm larger than the second, that is, the second edge will be equal to (x – 3) cm.

The third edge is 20 cm larger than the first, respectively, the third edge will be equal to (x + 20) cm.

It is known that the sum of the lengths of the edges of a rectangular parallelepiped is 80 m (or 8,000 cm), that is, the product of the sum of three dimensions of a rectangular parallelepiped by 4 is 8,000 cm.

Let’s compose and solve the equation:

4 (x + x – 3 + x + 20) = 8000.

4 (3 x + 17) = 8000.

12 x + 68 = 8000.

12 x = 8000 – 68.

12 x = 7932.

x = 7932: 12.

x = 661.

Thus, one of the edges of the rectangular parallelepiped is 661 cm.

Find the second edge: 661 – 3 = 658 (cm).

We will also find the third edge: 661 + 20 = 681 (cm).

Answer: the lengths of the edges of a rectangular parallelepiped are 661 cm, 658 cm and 681 cm.