The base of the pyramid MABCD is a square with a diagonal of 8. The MA rib is perpendicular to the base plane. Find the lengths of the side edges MB, MC, MD if MA = 6.
Since ABCD is a square, then by the Pythagorean theorem, AC ^ 2 = AD ^ 2 + CD ^ 2 = 2 * AD ^ 2.
AD ^ 2 = 64/2 = 32.
AD = 4 * √2 cm.
By condition, the lateral edge AM is perpendicular to the plane of the base of the pyramid, then the triangles AMB, AMC, AMD are rectangular.
By the Pythagorean theorem, we determine the lengths of the hypotenuses BM, BC, BD.
BM ^ 2 = AM ^ 2 + AB ^ 2 = 36 + 32 = 68. BM = 2 * √17 cm.
DM ^ 2 = AM ^ 2 + AD ^ 2 = 36 + 32 = 68. BM = 2 * √17 cm.
CM ^ 2 = AM ^ 2 + CM ^ 2 = 36 + 64 = 100. CM = 10 cm.
Answer: The lengths of the sides are equal to 2 * √17 cm, 2 * √17 cm, 10 cm.
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