A triangle with sides of length 6 and 7

HOME

Math Central

Quandaries & 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

Bill,

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.

Chris

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.