Find the perimeter of the rhombus if its diagonals are 16 cm and 12 cm.

It is known that the diagonals of a rhombus intersect at right angles and are halved at the point of intersection. Thus, the halves of the diagonals and the side form a right-angled triangle, for which, according to the Pythagorean theorem, we can write:

a ^ 2 = (d1 / 2) ^ 2 + (d2 / 2) ^ 2 = (16/2) ^ 2 + (12/2) ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100 = 102;

a = 10 cm – rhombus side.

The perimeter of a rhombus is equal to the sum of the lengths of its sides:

P = 4 * a = 4 * 10 = 40 cm.