Question

ABC is an equilateral triangle with side a. A point P is taken inside ABC. The sum of lengths of perpendicular from P to all the sides is

• A. greater than altitude from A to BC
• B. less than altitude from A to BC
• C. equal to altitude from A to B
• D. cant be determined

Answer 1

The correct option is C equal to altitude from A to B

The sum of the length perpendicular from $P$ as shown in the above figure.

As the length of perpendicular to every side will be same as it is an equilateral triangle thus the summation of all the sides will be equal to the perpendicular of $A$ and $B$.