If two sides of a triangle are 6 and 12, respectively, which of the fo

Official answer from veritas:

Solution: E.

If you know two sides of a triangle, the maximum area of the triangle can be obtained by setting these two sides as the base and height of a right triangle. For our triangle this gives us a maximum area of (6 * 12) / 2, or 36, so anything higher than this is invalid and the answer is (E). An alternative approach is to consider the minimum possible value of the triangle. Say we violated our third side rule and set the triangle's sides as 6, 12, and 18, respectively. Our "maximum" area here would be the set the base as 18, but since the triangle has no height -- the three sides only "fit together" as two parallel lines -- the height is 0 and the area is 0. But were we to extend one of the other two sides by an infinitesimally small amount, our area would be infinitesimally greater than 0, so presumably our minimum value is merely above zero. This means the greatest answer choice will be the number that violates the rule, and since no answer violates our minimum, (E) must again be the correct choice.