Question

State true or false:

In $△ABC$, $AB=BC=CA=2a$ and $AD$ is perpendicular to side $BC$, then $AD=2a\sqrt{3}$

• A. True
• B. False

Answer 1

Answer: (B)

In $△$s $ABD$ and $ACD$,
$\angle ADB=\angle ADC$ (Both ${90}^o$)
$AD=AD$ (Common)
$AB=AC$ (Given)
Hence, $△ABD\sim △ACD$ (SSA rule)
Hence, $BD=CD$ (By cpct)
Now, in triangle ABD,
$A{B}^2=A{D}^2+B{D}^2$ (From Pythagoras theorem)
$(2a{)}^2=A{D}^2+a^2$
$A{D}^2=3a^2$
$AD=a\sqrt{3}$