$$\triangle ABC$$ is an equilateral triangle in which $$D, E$$ and $$F$$ are the points on sides $$BC, AC$$ and $$AB$$, respectively, such that $$AD \perp BC, BE \perp AC$$ and $$CF \perp AB$$. Which of the following is true?

A

$$7AB^2 = 9AD^2$$

B

$$2AB^2 = 3AD^2$$

C

$$4AC^2 = 5BE^2$$

D

$$3AC^2 = 4BE^2$$