# Find the sides of a rhombus with a diagonal of 22 cm and 16 cm.

May 31, 2021 | education

| We use three properties of the rhombus. Firstly, all sides of the rhombus are equal, so we only need to find the length of one of them.

Secondly, the diagonals of the rhombus are halved by the intersection point. Find half of each diagonal:

22/2 = 11;

16/2 = 8.

Third, the diagonals of the rhombus intersect at right angles. This means that the diagonals split the rhombus into 4 identical right-angled triangles. Then the length of the side of the rhombus can be found by the Pythagorean theorem. The legs in this case are half of the diagonals, and the hypotenuse is the side of the rhombus. The square of the side of the rhombus is:

11 * 11 + 8 * 8 = 185.

The side of the rhombus is √185.

Answer: √185.

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