The sides of the base of the rectangular parallelepiped are 6 cm and 8 cm. The height of the parallelepiped is 12 cm. Find the dialonals of the parallelepiped.
Since the parallelepiped is rectangular, all of its faces are rectangles.
Let us construct the diagonals AC and BD at the base of the parallelepiped.
By the Pythagorean theorem in a right-angled triangle ABD, we determine the length of the hypotenuse BD.
BD ^ 2 = AB ^ 2 + AD ^ 2 = 36 + 64 = 100.
ВD = 10 cm.
Since ABCD is a rectangle, its diagonals are equal, AC = BD = 10 cm.
In a right-angled triangle АА1С, according to the Pythagorean theorem, we determine the length of the diagonal А1С.
A1C ^ 2 = AC ^ 2 + AA1 ^ 2 = 100 + 144 = 244.
A1C = 2 * √61 cm.
DB1 = A1C1 = 2 * √61 cm.
Answer: The diagonals of the parallelepiped are 2 * √61 cm.
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