The base of the pyramid is KABCD-square, the diagonal of which is 8 √2. The edge of KB is perpendicular

| June 10, 2021 | education

The base of the pyramid is KABCD-square, the diagonal of which is 8 √2. The edge of KB is perpendicular to the plane of the base. Find the lengths of the side ribs KA, KD, KC, if KB = 6

Since the edge KB is perpendicular to the plane of the base of the pyramid, the triangles ABK, CBK, DBK are rectangular.

In a right-angled triangle DВК, about the Pythagorean theorem, we determine the length of the hypotenuse КD.

KD ^ 2 = BK ^ 2 + BD ^ 2 = 36 + 128 = 164.

КD = 2 * √41 cm.

In a right-angled triangle ABC AB = BC, then by the Pythagorean theorem, 2 * AB ^ 2 = 2 * BC ^ 2 = AC ^ 2 = 128.

AB ^ 2 = BC ^ 2 = 64.

AB = BC = 8 cm.

In a right-angled triangle ABK, according to the Pythagorean theorem, AK ^ 2 = AB ^ 2 + BK ^ 2 = 64 + 36 = 100.

AK = 10 cm.

Rectangular triangles ABK and СBK are equal in two legs, then CK = AC = 10 cm.

Answer: The side ribs are 10 cm, 10 cm, 2 * √41 cm.



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