In a rectangular parallelepiped ABCDA1B1C1D1. it is known that BD1 = 6, CC1 = 2, AD = √7.
| July 19, 2021 | education
In a rectangular parallelepiped ABCDA1B1C1D1. it is known that BD1 = 6, CC1 = 2, AD = √7. find the length of the edge D1C1.
Let’s draw the diagonal CB1 of the side face BCC1B1.
In a parallelepiped, the lengths of the opposite edges are equal, then BC = AD = √7 cm, BB1 = CC1 = 2 cm.
In a right-angled triangle CBB1, according to the Pythagorean theorem, CB1 ^ 2 = BC ^ 2 + BB1 ^ 2 = 7 + 4 = 11.
In a right-angled triangle CB1D, according to the Pythagorean theorem, we determine the length of the leg CD.
CD ^ 2 = DB1 ^ 2 – CB1 ^ 2 = 36 – 16 = 25.
CD = 5 cm.
Then the length of the edge is D1C1 = CD = 5 cm.
Answer: The length of the rib D1C1 = 5 cm.
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