Originally Posted by

**findmehere.genius** yet another question for someone willing to help for I am tired wasting four long pages....

**Q.There is a point inside an equilateral triangle which is at distances**

**1, 2 and 3 from the three sides. The area of the triangle is**

**A**

not uniquely determinable

**B 6 root3**

**C 6**

**D 12 root3**

In an equilateral triangle,

if you know the perpendicular distances to all three sides (which is given),

then that sum will equal the altitude (h) of the triangle (which is 1+2+3 = 6).

The base (or 1 side of the triangle) is $\displaystyle 2 h \tan(30deg) $

$\displaystyle

\tan(30deg) = \dfrac{ \sqrt{3} } {3}

$

Thus:

$\displaystyle \text{Area} = h^2 \cdot \dfrac{ \sqrt{3}} {3} $ = $\displaystyle 6^2 \cdot \dfrac{ \sqrt{3}} {3} \,\, = \,\, 12 \cdot \sqrt{3} $

as shown previously.

.