# 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: AC^{2 }+ BD^{2} = 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, 2AB^{2 }+ 2BC^{2 }= AC^{2 }+ BD^{2}

AC^{2 }+ BD^{2} = 2x^{2} + 2x^{2} = 4x^{2}

So, the sides and diagonals of a rhombus are related by the equation AC^{2 }+ BD^{2} = 4 (side)^{2}

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 d_{1} and d_{2}.

d_{1} × d_{2} = 2 × Area of Rhombus