The sum of the lengths of all edges of a rectangular parallelepiped is 144 cm, the sum of width

The sum of the lengths of all edges of a rectangular parallelepiped is 144 cm, the sum of width and height is 21 cm, and the sum of length and width is 27 cm. What is the volume of this parallelepiped?

1. Find the lengths of the sides of this parallelepiped. Let’s denote the length, width and height of the parallelepiped by the letters a, b and c, respectively. In total, the parallelepiped has 12 edges; in a rectangular parallelepiped 4 edges of length a, 4 edges of length b and 4 edges of length c. Then the sum of the lengths of all edges can be written as 4 * (a + b + c).

2. According to the problem statement, we compose and solve the system of equations:

4 * (a + b + c) = 144;

b + c = 21;

a + b = 27;

3. Transforming the first equation, we get a + b + c = 144/4 = 36.

Then c = (a + b + c) – (a + b) = 36 – 27 = 9 cm.

b = 21 – c = 21 – 9 = 12 cm;

a = 27 – b = 27 – 12 = 15 cm.

4. The volume of a rectangular parallelepiped is equal to the product of the area of ​​the base, ie. product a * b * c = 15 * 12 * 9 = 1620 cm3.

Answer: the volume of the parallelepiped is 1620 cm3.