In rectangular parallelepiped ABCDA1B1C1D1 it is known that DD1 = 1, CD = 2, AD = 2.
| May 7, 2021 | education
In rectangular parallelepiped ABCDA1B1C1D1 it is known that DD1 = 1, CD = 2, AD = 2. Find the length of the diagonal CA1.
Let’s construct the diagonal of the AC base. In a right-angled triangle ACD, according to the Pythagorean theorem, AC ^ 2 = AD ^ 2 + DC ^ 2 = 2 ^ 2 + 2 ^ 2 = 4 + 4 = 8.
In a right-angled triangle ACA1, side AA11 = DD1 = 1 cm, then by the Pythagorean theorem,
CA1 ^ 2 = AC ^ 2 + AA1 ^ 2 = 8 + 1 = 9.
CA1 = 3 cm.
Answer: The length of the hypotenuse CA1 is 3 cm.
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