The perimeter of the rhombus is 40 cm, and one of its diagonals is 12 cm, find the second diagonal of the rhombus

Since in any rhombus all its sides are equal, and, according to the condition of the problem, the sum of the lengths of all four sides of this rhombus is 40 cm, the length of the side of this rhombus is 40/4 = 10 cm.

Each rhombus is divided by its diagonals into 4 identical right-angled triangles, the legs of which are halves of the diagonals of the rhombus, and the hypotenuses are the side of the rhombus.

Consider one of these triangles.

Denoting the length of the unknown diagonal through a, we can compose the following equation:

(a / 2) ^ 2 + (12/2) ^ 2 = 10 ^ 2,

solving which, we get:

a ^ 2/4 + 36 = 100;

a ^ 2/4 = 100 – 36;

a ^ 2/4 = 64;

a ^ 2 = 64 * 4;

a ^ 2 = 256;

a ^ 2 = 16 ^ 2;

a = 16 cm.

Answer: 16 cm.