The side of the rhombus is 10 cm and one of its diagonals is 16 cm. Find the second diagonal

A rhombus is a parallelogram in which all sides are equal.

Let’s recall some of the properties of a rhombus that are necessary to solve this problem:

the diagonals of the rhombus are mutually perpendicular;
the diagonals are halved by the intersection point.
We have a rhombus ABCD, AB = BC = CD = DA = 10 cm, BD = 16 cm. Find AC.

Point O is the point of intersection of the diagonals of the rhombus, therefore BO = OD = BD / 2 = 16/2 = 8 cm, AO = OC.

△ ABO – rectangular.

By the Pythagorean theorem:

AB ^ 2 = BO ^ 2 + AO ^ 2.

Hence AO = √ (AB ^ 2 – BO ^ 2) = √ (10 ^ 2 – 8 ^ 2) = √ (100 – 64) = √36 = 6 cm.

Then OC = AO = 6 cm,

AC = OC + AO = 6 + 6 = 12 cm.

Answer: 12 cm.