The perimeter of the rhombus = 20 cm, and one of its diagonals = 8 cm. Find the second diagonal.

By condition, the perimeter of the rhombus is 20 cm, then its side:
a = 20/4 = 5 (cm).
Consider one of four equal right-angled triangles that form when the diagonals intersect. It knows the hypotenuse – the side of the rhombus (5 cm) and the leg – half of the diagonal given by the condition (4 cm). Unknown leg – this will be half of the second diagonal:
√ (25 – 16) = √9 = 3 (cm), the whole diagonal is 6 cm.
Answer: the second diagonal of the rhombus is 6 cm.