In the rectangular parallelepiped ABCBA1B1C1B1 it is known that АА1 = 24, С1D1 = 3, BC = 12. Find the length of AC1.

Because the figure is a rectangular parallelepiped, from the AC1 diagonal will be the hypotenuse in the ACC1 triangle. To find it, you must first find out what the AC leg is. At the base of the figure lies a rectangle, which means that all the corners are straight. Therefore, AC is the hypotenuse in the ABC triangle. Because the opposite faces are equal at the parallelepiped, which means AB = C1D1 = 3, and BC = 12 by condition. Find AC:

AC = √12 ^ 2 + 3 ^ 2 = √153.

Because CC1 = AA1 = 24, find AC1:

AC1 = √153 + 242 = √729 = 27.

Answer: AC1 = 27.