In the rectangular parallelepiped ABCDA1B1C1D1 it is known that AD = 12, CC1 = 3√39, AB = 9.
| April 7, 2021 | education
In the rectangular parallelepiped ABCDA1B1C1D1 it is known that AD = 12, CC1 = 3√39, AB = 9. Find the length of the diagonal AC1.
Draw a diagonal AC at the base of the parallelepiped.
The base of ABCD is a rectangle, then triangle ACD is rectangular. Then, by the Pythagorean theorem, AC ^ 2 = AD ^ 2 + CD ^ 2 = 144 + 81 = 225.
AC = 15 cm.
Triangle ACC1 is rectangular, then AC1 ^ 2 = AC ^ 2 + CC1 ^ 2 = 225 + 351 = 576.
AC1 = 24 cm.
Answer: The length of the AC1 diagonal is 24 cm.
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