# The sides of the base of the rectangular parallelepiped are 6 cm and 8 cm.

**The sides of the base of the rectangular parallelepiped are 6 cm and 8 cm. The height of the parallelepiped is 12 cm. Find the dialonals of the parallelepiped.**

Since the parallelepiped is rectangular, all of its faces are rectangles.

Let us construct the diagonals AC and BD at the base of the parallelepiped.

By the Pythagorean theorem in a right-angled triangle ABD, we determine the length of the hypotenuse BD.

BD ^ 2 = AB ^ 2 + AD ^ 2 = 36 + 64 = 100.

ВD = 10 cm.

Since ABCD is a rectangle, its diagonals are equal, AC = BD = 10 cm.

In a right-angled triangle АА1С, according to the Pythagorean theorem, we determine the length of the diagonal А1С.

A1C ^ 2 = AC ^ 2 + AA1 ^ 2 = 100 + 144 = 244.

A1C = 2 * √61 cm.

DB1 = A1C1 = 2 * √61 cm.

Answer: The diagonals of the parallelepiped are 2 * √61 cm.