If two sides of a triangle are 6 and 10, respectively, which of the following could NOT be the area of this triangle?  Pick
A) 1  B) 6  C) 17  D) 38  E) 29
For this question it would be helpful to know the largest area that this triangle could be, given the two sides of 6 and 10.   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)10 * 6 -or- (.5)6 * 10 will result in a maximum area of 30 for the triangle; therefore, the triangle could never have an area of 38.   38
<result>D</result>
If two sides of a triangle are 6 and 10, respectively, which of the following could NOT be the area of this triangle?