You are given a rectangular parallelepiped. The sum of the lengths of all its ribs is 152 cm.

You are given a rectangular parallelepiped. The sum of the lengths of all its ribs is 152 cm. The sum of the height and length is 30 cm. And the height and width are 20 cm. What is the volume of the parallelepiped?

Let the length of the parallelepiped be a, width b, and height h. Then, by hypothesis, we can write the following equalities:

4a + 4b + 4c = 152;

a + h = 30;

b + h = 32.

Let us express a and b through h and substitute them in the first expression:

a = 30 – h;

b = 32 – h;

4 (30 – h) + 4 (32 – h) + 4h = 152;

120 – 4h + 128 – 4h + 4h = 152;

4h = 96;

h = 24 cm.

Now let’s find the rest of the sides:

a = 30 – h = 30 – 24 = 6 cm.

b = 32 – h = 32 – 24 = 8 cm.

Now we can find the volume by multiplying all sides:

24 * 6 * 8 = 1152 cm3.

Answer: the volume of the parallelepiped is 1152 cm3.