14. An equilateral triangle is divided into three congruent trapezoids, as shown in the figure. If the perimeter of each trapezoid is $10+5 \sqrt{3}$, what is the side length of the triangle?
Answer: $6+3 \sqrt{3}$ units
Solution: Each of the trapezoids will have the following interior angles.
We therefore have an isosceles trapezoid. By the manner in which the trapezoids are tiled, the shorter base and the two legs will all have the same length; let it be $a$. The longer base is then equal to $a+\frac{a}{2}+\frac{a}{2}=2 a$. Therefore
$$
\begin{aligned}
a+a+a+2 a & =10+5 \sqrt{3} \\
5 a & =10+5 \sqrt{3} \\
a & =2+\sqrt{3}
\end{aligned}
$$

The side length of a triangle is $a+2 a=3 a=6+3 \sqrt{3}$.