Question

If $△ABC$ is an equilateral triangle such that $AD$ is perpendicular to $BC$, then $A{D}^2=$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

In $△ABC,AD\perp BC$.

$\Rightarrow A{C}^2=A{D}^2+C{D}^2$ [By Pythagoras Theorem]

$\Rightarrow A{D}^2=A{C}^2-C{D}^2$

$\Rightarrow A{D}^2=B{C}^2-C{D}^2$ [since $AC=BC$]

$\Rightarrow A{D}^2=(2CD{)}^2-C{D}^2$ [since $BC=2CD$]

$\Rightarrow A{D}^2=3C{D}^2$