# In rectangular parallelepiped ABCD A1B1C1D1 it is known that AC1 = 18, AB = 16, A1D1 = 2.

July 31, 2021 | education

| **In rectangular parallelepiped ABCD A1B1C1D1 it is known that AC1 = 18, AB = 16, A1D1 = 2. Find the length of the edge AA1.**

To solve this problem, let us denote a straight parallelepiped as ABCDA1B1C1D1.

Consider a triangle A1D1C1, it is rectangular, with sides A1D1 = 2, C1D1 = AB = 16.

Let us find the A1C1 side behind Pythagoras c.: A1C1 ^ 2 = 4 ^ 2 + 16 ^ 2, where A1C1 = 2√65.

Consider a triangle АА1С1, in which the angle А1 = 90, АА1 is an unknown leg, AC1 = 18, А1С1 = 2√65.

Let us find the side AA1 behind Pythagoras’ c. AA1 ^ 2 = 18 ^ 2 – 2√65 ^ 2, where AA1 = 8.