# The width of the rectangular parallelepiped is 2 2/5 dm, the length is 1 7/8 times the width, and the height is 1 1/6 dm

**The width of the rectangular parallelepiped is 2 2/5 dm, the length is 1 7/8 times the width, and the height is 1 1/6 dm less than the length. What is the volume of this rectangular parallelepiped?**

The volume of a rectangular parallelepiped is equal to the product of its three dimensions: length, width and height.

1) What is the length of a rectangular parallelepiped?

2 2/5 * 1 7/8 = (5 * 2 + 2) / 5 * (8 * 1 + 7) / 8 = 12/5 * 15/8 = 3/1 * 3/2 = 9/2 = 4 1/2 (dm) – reduce 12 and 8 by 4; reduce 15 and 5 by 5.

2) What is the height of a rectangular parallelepiped?

4 1/2 – 1 1/6 = 4 3/6 – 1 1/6 = 3 2/6 = 3 1/3 (dm)

3) What is the volume of a rectangular parallelepiped?

V = 2 2/5 * 4 1/2 * 3 1/3 = 12/5 * 9/2 * 10/3 = 36 (dm ^ 3) – we reduce 10 and 2 * 5 by 10; reduce 9 and 3 by 3.

Answer. 36 dm ^ 3.