In a rectangular parallelepiped, the sides of the base are 5 and 12, and the area of the diagonal section is 78

univerkov | January 11, 2021 | education

In a rectangular parallelepiped, the sides of the base are 5 and 12, and the area of the diagonal section is 78. Find the height of the parallelepiped.

The diagonal section of a straight parallelepiped is a rectangle АА1С1С.
Since a rectangle lies at the base of a rectangular parallelepiped, the ACD triangle is rectangular, and then, according to the Pythagorean theorem, AC ^ 2 = AB ^ 2 + AD ^ 2 = 25 + 144 = 169.
AC = 13 cm.
Through the area of the diagonal section and the length of one of its sides, we determine the length of the other side.
Ssech = АС * АА1.
AA1 = Ssection / AC = 78/13 = 6 cm.
Answer: The height of the parallelepiped is 6 cm.

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