Length of Median of Trapezoid
Source:
February 11, 2009
geometrytrapezoid
Problem Statement
An equilateral triangle whose side is is divided into a triangle and a trapezoid by a line drawn parallel to one of its sides. If the area of the trapezoid equals one-half of the area of the original triangle, the length of the median of the trapezoid is:
(A)\ \frac{\sqrt{6}}{2} \qquad
(B)\ \sqrt{2} \qquad
(C)\ 2\plus{}\sqrt{2} \qquad
(D)\ \frac{2\plus{}\sqrt{2}}{2} \qquad
(E)\ \frac{2\sqrt{3}\minus{}\sqrt{6}}{2}