Question

In an equilateral triangle $ABC,$ if $AD\perp BC$, then

• A. 2 AB² = 3 AD²
• B. 4 AB² = 3 AD²
• C. 3 AB² = 4 AD²
• D. 3 AB² = 2 AD²

Answer 1

The correct option is C

3 AB² = 4 AD²

Since, $\Delta ABC$ is equilateral

Therefore, $BD=\frac{AB}{2}$

${AB}^2={BD}^2+{AD}^2$ [by Pythagoras Theorem]

$\Rightarrow {AB}^2={\left(\frac{1}{2}AB\right)}^2+{AD}^2$

$\Rightarrow {AB}^2=\frac{{AB}^2}{4}+{AD}^2$

$4{AB}^2={AB}^2+4{AD}^2$

$\Rightarrow 3{AB}^2=4{AD}^2$