Find the sum of the lengths of all the edges of a rectangular parallelepiped, the dimensions of which are 13cm, 16cm, 21cm.

Let’s denote the dimensions of the parallelepiped: a – length, b – width, c – height.

Given: a = 13 cm, b = 16 cm, c = 21 cm.

Find: the sum of the lengths of all edges of a rectangular parallelepiped.

Decision:

Since a rectangular parallelepiped has 4 heights, 4 widths and 4 lengths (equal to each other), then:

1) 4 * 13 = 52 (cm) – the sum of the lengths of the parallelepiped;

2) 4 * 16 = 64 (cm) – the total value of the parallelepiped’s width;

3) 4 * 21 = 84 (cm) – the sum of the heights of the parallelepiped;

4) 52 + 64 + 84 = 200 (cm) – the sum of the lengths of all the edges of the rectangular parallelepiped.

Thus, to find the sum of the lengths of all edges of a rectangular parallelepiped, you can derive the formula: Z = 4a + 4b + 4c (where Z is the sum of the lengths of the edges).

Answer: 200 cm.