12. A point is chosen inside an equilateral triangle. From this point we draw three segments parallel to the sides, as shown. The lengths of the segments are $2 \mathrm{~m}, 3 \mathrm{~m}$ and $6 \mathrm{~m}$. What is the perimeter of the triangle?
A $22 \mathrm{~m}$
B $27 \mathrm{~m}$
C $33 \mathrm{~m}$
D $39 \mathrm{~m}$
E $44 \mathrm{~m}$
Solution
C

Extend the segments through the point to the border of the shape. On the base we have an equilateral triangle and two parallelograms. Hence, the sides of the original triangle have length $2 \mathrm{~m}+3 \mathrm{~m}+6 \mathrm{~m}=11 \mathrm{~m}$. So the perimeter of the triangle is $33 \mathrm{~m}$.