In rectangular parallelepiped ABCDA1B1C1D1 it is known that BB1 = 12cm, A1B1 = 21cm

In rectangular parallelepiped ABCDA1B1C1D1 it is known that BB1 = 12cm, A1B1 = 21cm, AD = 16cm. Find the length of the diagonal AC1.

Let’s draw a diagonal of the base of the AC. In a right-angled triangle ACD, AB = A1B1 = 21 cm, BC = AD = 16 cm, then, according to the Pythagorean theorem, AC ^ 2 = AB ^ 2 + BC ^ 2 = 21 ^ 2 + 16 ^ 2 = 441 + 256 = 697 …

In a right-angled triangle ACC1, side CC1 = BB1 = 12 cm, then by the Pythagorean theorem,

AC1 ^ 2 = AC ^ 2 + CC1 ^ 2 = 697 + 144 = 841.

AC1 = 29 cm.

Answer: The length of the hypotenuse AC1 is 29 cm.