How to find the length of a diagonal of a rhombus?

We will show two cases of the relationship between two diagonals of a rhombus.

Answer: AC² + BD² = 4 (side)², AC × BD = 2 × Area of Rhombus

Let ABCD be a rhombus with diagonals AC and BD.

Explanation:

Case 1: When the side of a rhombus is given,

Let the side of a rhombus be x units.

By parallelogram law, 2AB² + 2BC² = AC² + BD² 

AC² + BD² = 2x² + 2x² = 4x²

So, the sides and diagonals of a rhombus are related by the equation AC² + BD² = 4 (side)²

So, the diagonal of a rhombus can be calculated when one side and one diagonal are given.

Case 2: When the area of a rhombus is given,

The area of a rhombus is given by the formula: Area of Rhombus = (Product of Diagonals) / 2

Let the diagonals of a rhombus be d1 and d2.

d1 × d2 = 2 × Area of Rhombus

So, you can use any of the two formulas to find the diagonal of a rhombus.