The side of the rhombus is 26 cm, its large diagonal is 48 cm. Find the length of the smaller diagonal.

For the solution, we will use the property of the rhombus, according to which the diagonals of the rhombus at the point of their intersection are halved.

Consider a right-angled triangle AOB, in which the hypotenuse AB is equal to the length of the rhombus side 26 cm, and the leg AO is equal to half the length of the larger diagonal of the rhombus 48/2 = 24. Find the second leg OB of this triangle, which will be half of the desired diagonal. By the Pythagorean theorem AB ^ 2 = AO ^ 2 + OB ^ 2.

OB ^ 2 = AB ^ 2 – AO ^ 2 = 26 ^ 2 – 24 ^ 2 = 100.

OA = √100 = 10.

Then the required diagonal BD = 2 x AO = 20 cm.

Answer: 20 cm.