One internal angle of a rhombus of side 12 cm is 120°. What is the length of its longer diagonal?

Given : ABCD is a rhombus with AB = 12 cm and $$\angle$$ ABC = 120°

To find : AC = ?

Solution : Diagonals of a rhombus bisect each other at 90° and bisect the angles opposite to them.

=> $$\angle$$ OBA = 60°

In $$\triangle$$ AOB, $$sin (\angle OBA) = \frac{OA}{AB}$$

=> $$sin(60) = \frac{OA}{12}$$

=> $$\frac{\sqrt{3}}{2} = \frac{OA}{12}$$

=> $$OA = 6\sqrt{3}$$ cm

Since, the diagonals bisect each other, => $$AC = 2 \times (OA)$$

= $$2 \times 6\sqrt{3} = 12\sqrt{3}$$ cm

=> Ans - (D)