Question

In an equilateral triangle ABC, the ratio of length of the perpendicular AD to side AB is

• A. 1/2
• B. √3/2
• C. √2
• D. √3

Answer 1

The correct option is B

√3/2

Let each side of the equilateral triangle be a. A perpendicular bisector AD (which is the median and angle bisector) is drawn. In $△$ABD

$A{D}^2$ = $A{B}^2$ - $B{D}^2$ = $a^2-\frac{a^2}{4}$ = $\frac{3a^2}{4}$

AD = $\frac{\sqrt{3}a}{2}$

$\frac{AD}{AB}$ = $\frac{\sqrt{3}}{2}$