question_answer

\[\Delta ABC\] is an equilateral triangle with each side of length \[\text{2p}\]. If \[AD\bot BC\] the then value of AD is:

A) \[\sqrt{3}\]

B) \[\sqrt{3}p\]

C) \[2p\]

D) \[4p\]

Correct Answer: B

Solution :

[b] Given an equilateral triangle ABC in which.

\[AB=BC=CA=2p\]

and     \[AD\bot BC\]

In \[\Delta ADB,\] \[A{{B}^{2}}=A{{D}^{2}}+B{{D}^{2}}\]

(By Pythagoras theorem)

\[{{(2P)}^{2}}=A{{D}^{2}}+{{p}^{2}}\]

\[A{{D}^{2}}=\sqrt{3}p\]