The base of the straight prism is a rhombus. The diagonals of the prism are 8 and 5 cm. Height 2 cm. Find the side of the base.

Let us construct the diagonals AC and BD at the base of the prism.

Triangles DBB1 and CAA1 are rectangular, in which, according to the Pythagorean theorem, we determine the lengths of the legs AA1 and BB1.

AC ^ 2 = CA1 ^ 2 – AA1 ^ 2 = 64 – 4 = 60.

AC = √60 = 2 * √15 cm.

BD ^ 2 = DB1 ^ 2 – BB1 ^ 2 = 25 – 4 = 21.

ВD = √21 cm.

The diagonals of the ABCD rhombus at the intersection point are halved and intersect at right angles.

Then ОD = ВD / 2 = √21 / 2, OC = АС / 2 = √15 cm.

In a right-angled triangle COD, according to the Pythagorean theorem:

CD ^ 2 = OD ^ 2 + OC ^ 2 = (21/4) + 15 = (21 + 60) / 4 = 81/4.

CD = 9/2 = 4.5 cm.

Answer: The length of the side of the base is 4.5 cm.