One diagonal of a rhombus is half the other. If the length of the side of the rhombus is 20 cm, what is the area of the rhombus?

AC and BD are diagonals of the rhombus ABCD with side = 20 cm

One diagonal of a rhombus is half the other, let AC = $$4x$$ cm

=> BD = $$2x$$ cm

Diagonal of a rhombus perpendicularly bisect each other.

=> OD = $$x$$ cm and OC = $$2x$$ cm

In $$\triangle$$ OCD, => $$(OC)^2 + (OD)^2 = (CD)^2$$

=> $$(2x)^2 + (x)^2 = (20)^2$$

=> $$4x^2 + x^2 = 400$$

=> $$x^2 = \frac{400}{5} = 80$$

$$\therefore$$ Area of rhombus = $$\frac{1}{2} \times$$ Product of diagonals

= $$\frac{1}{2} \times 4x \times 2x$$

= $$4x^2 = 4 \times 80 = 320 cm^2$$

=> Ans - (A)