Math CentralQuandaries & Queries


Question from bill, a teacher:

If I have a triangle with sides 6 and 7, which of the following is a possible area?
The answers are 13 and 21, but not 24.
I know this is because of a possible range of heights, but how do I calculate the range of heights?
This is an SAT question. Thanks


Let AB = 6 be the base of your triangle, and AC = 7 be the second side. The height h is the perpendicular distance from C to the side AB. The area of triangle ABC is (1/2) base x height = 3h. Open a open a new window and move C around to determine how big and how small h can become.


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