GRE Sample Test 4 Quantitative Reasoning 2

The area of a triangle equals $\frac{1}{2}$ x base x height.
Triangles ACE and ABD have the same height, because they have the same apex point A. The problem states that their areas are equal, so they must have the same base, too. Thus, EC = DB and ED = CB. Since triangle ABE is equilateral, you also know that AE = AB. This means that sides AD and AC are equal as well. If they weren’t, one of ED or CB would have to be longer than the other, and you already know they’re equal. The answer is (C).