The sides of the parallelogram are 10 cm and 24 cm and one of its diagonals is 26 cm Find the length of the other diagonal.

Let one of the sides of the parallelogram be a = 10 cm, the second b = 24 cm, the diagonal c = 26 cm, and the second diagonal d is unknown. To find it, we will use the property of the parallelogram diagonals, which consists in the fact that the sum of the squares of the sides of the parallelogram is equal to the sum of the squares of its sides:

c ^ 2 + d ^ 2 = 2 * (a ^ 2 + b ^ 2).

Substituting the values, we get:

26 ^ 2 + d ^ 2 = 2 * (10 ^ 2 + 24 ^ 2);

d ^ 2 = 2 * (100 + 576) – 676;

d ^ 2 = 2 * 676 – 676;

d ^ 2 = 676;

d = 26 cm.

Answer: the length of the other diagonal of the parallelogram is 26 cm.