In the rectangle ABCD, it is known that BD = 8 cm, AD = 10 cm. Find the perimeter of the BOC triangle.

This will require the properties of the rectangle:

In a rectangle, opposite sides are equal; the diagonals are equal and the intersection point is halved.

AD = 10 cm (by condition), the opposite side of the BC is also 10 cm.

The triangle BОС includes two more sides – BO and CO, these are halves of the diagonals. One diagonal BD = 8 cm (by condition), which means that the second diagonal of the AC is also 8 cm, and their halves are 4 cm each.

In a triangle BОС: ВС = 10 cm, BО = 4 cm, СО = 4 cm.

It remains to find the perimeter, that is, the sum of the sides: P = 10 + 4 + 4 = 18 cm.