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.
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