In a rectangular parallelepiped, the sides of the bases are 8 cm and 6 cm, and the diagonal is 26 cm. Find the side rib.

Since the parallelepiped is rectangular, a rectangle lies at its base, and the side edges are perpendicular to the plane of its base.

Let us draw the diagonal of the base AC, the length of which is determined by the Pythagorean theorem.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 64 + 36 = 100.

AC = 20 cm.

Triangle AA1C is rectangular, then AA1 ^ 2 = A1C ^ 2 – AC ^ 2 = 676 – 100 = 576.

AA1 = 24 cm.

Second way.

In a rectangular parallelogram, the square of its diagonal is equal to the sum of the squares of the lengths of its sides.

A1C ^ 2 = AA1 ^ 2 + AD ^ 2 + CD ^ 2.

AA1 ^ 2 = A1C ^ 2 – AD ^ 2 + CD ^ 2 = 676 – 64 – 36 = 576.

AA1 = 24 cm.

Answer: The side rib is 24 cm.