The sum of the lengths of all the edges of a rectangular parallelepiped is 60 cm

The sum of the lengths of all the edges of a rectangular parallelepiped is 60 cm, the sum of width and height is 10 cm, and the sum of length and width is 11 cm. What is the volume of this parallelepiped?

Suppose that the length of this parallelepiped is a, the width is b and the height is c.

As you know, a rectangular parallelepiped has 12 edges, 4 of which are equal to its length, 4 are equal to the width and 4, respectively, to the height.

Thus, we get:

4 * (a + b + c) = 60 (cm),

a + b + c = 15 (cm).

It is known that b + c = 10 cm, therefore, a = 15 – 10 = 5 (cm).

a + b = 11 cm, so c = 15 – 11 = 4 (cm), and b = 11 – 5 = 6 (cm).

The volume of a rectangular parallelepiped is equal to the product of its measurements, that is, in our case it is equal to:

V = 5 * 6 * 4 = 120 cm3.

Answer: 120 cm3.