If two sides of a triangle are 3 and 12, respectively, which of the following could NOT be the area of this triangle?
Choose the correct option:
A) 1
B) 6
C) 17
D) 29
E) 16
For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 3 and 12.   We know that the area of a triangle will be maximized when two sides are perpendicular to each other (consult Bunuel's drawing above). Thus we have a max area being equal to one half the base times the height, either (.5)12 * 3 -or- (.5)3 * 12 will result in a maximum area of 18 for the triangle; therefore, the triangle could never have an area of 29.   29
<result>D</result>
If two sides of a triangle are 3 and 12, respectively, which of the following could NOT be the area of this triangle?