Question

In an equilateral triangle if $a,bandc$ denote the lengths of the perpendicular from $A,BandC$ respectively on the opposite sides, then

• A. $a>b>c$
• B. $a>b<c$
• C. $a<b<c$
• D. $a=b=c$

Answer 1

The correct option is D

$a=b=c$

Explanation of the Correct Option:

Option (D): $a=b=c$

Given that $△ABC$ is an equilateral triangle, where $a,b,andc$ denotes the length of the perpendiculars from $A,BandC$ to the opposite sides.

Length of perpendiculars$=\frac{\sqrt{3}}{2}\times \left(\mathrm{side}\right)$

$\because$Lengths of the perpendiculars from the vertices to the opposite sides are always equal in an equilateral triangle.

$\therefore a=b=c$

Therefore, option (D) is the correct answer.