The lateral edge of a straight parallelepiped is 5 cm, the sides of the base are 6 cm and 8 cm

| August 15, 2021 | education

The lateral edge of a straight parallelepiped is 5 cm, the sides of the base are 6 cm and 8 cm, and one of the diagonals of the base is 12 cm. Find the diagonal of the parallelogram.

Since, by condition, the parallelepiped is a straight line, the lateral edges are perpendicular to the base, therefore, the ACC1 triangle is rectangular. Then, by the Pythagorean theorem, AC1 ^ 2 = AC ^ 2 + CC1 ^ 2 = 12 ^ 2 + 5 ^ 2 = 144 + 25 = 169.

AC1 = 13 cm.

Since the sum of the squares of the diagonals of the parallelogram is equal to the doubled sum of the squares of its sides, then at the base of ABCD we determine the length of the diagonal BD.

BD ^ 2 + AC ^ 2 = 2 * (AB ^ 2 + BC ^ 2).

BD ^ 2 + 144 = 2 * (36 + 64) = 200.

BD ^ 2 = 200 – 144 = 56.

From the right-angled triangle В1ВD we define, according to the Pythagorean theorem, the hypotenuse В1D.

B1D ^ 2 = BB1 ^ 2 + BD ^ 2 = 25 + 56 = 81.

B1D = 9 cm.

Answer: The diagonals of the parallelepiped are 9 cm and 13 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.