Question

P is point in the interior of an equilateral triangle with side $a$ units. If $P_1,P_2$ and $P_3$ are the distance of $P$ from the three sides of the triangle, the $P_1+P_2-P_3$

• A. Equals $\frac{2a}{3}$ units
• B. Equals $\frac{a\sqrt{3}}{2}$ units
• C. Is more than $a$ unit
• D. Cannot be determined unless the location of P specified

Answer 1

The correct option is B Equals $\frac{a\sqrt{3}}{2}$ units

Area of equilateral $\Delta =\frac{\sqrt{3}}{4}{a}^2=\frac{1}{2}a(P_1+P_2+P_3)$
$=\frac{\sqrt{3}}{4}{a}^2\times \frac{2}{a}=P_1+P_2+P_3$
$=\frac{\sqrt{3}a}{2}=P_1+P_2+P_3$