Question

In equilateral $\Delta ABC,AD$ is altitude. Then $4A{D}^2$ equals ________.

• A. $2B{D}^2$
• B. $2D{C}^2$
• C. $B{C}^2$
• D. $3A{B}^2$

Answer 1

The correct option is D $3A{B}^2$

Given $AB=BC=AC=a$ units (say)

$AD$ is the altitude,say,of $h$ units

$BD=CD=\frac{a}{2}$ (in an equivalent triangle AD bisects BC)

Using Pythagoras theorem,

$\frac{a^2}{4}+h^2=a^2=>4h^2=3a^2=>4{AD}^2=3{AB}^2=3{BC}^2=3{AC}^2$