in rectangular parallelepiped ABCDA’B’C’D ‘is known, BD’ = 21, CD = 16, B’C ‘= 11. find the length of the edge BB’
| January 20, 2021 | education
Construct the diagonal B1D1.
Since all the side faces of the parallelepiped are rectangles, then D1C1 = DС = 16 cm.
Then from the right-angled triangle B1C1D1, by the Pythagorean theorem, we define the hypotenuse B1D1. B1D1 ^ 2 = B1C1 ^ 2 + C1D1 ^ 2 = 121 + 256 = 377.
B Triangle BB1D1 is rectangular, then BB1 ^ 2 = VD1 ^ 2 – B1D1 ^ 2 = 441 – 377 = 64.
BB1 = 8 cm.
Answer: The length of the rib BB1 is 8 cm.
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