 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from Chris, a student: Two of the altitudes of a scalene triangle ABC have length 4 and 12. If the length of the third altitude is also an integer, what is the biggest that it can be? Justify all of your conclusions. |
Chris,
You need two facts here:
- base times altitude equals twice the area of a triangle, and
- the sides of the triangle must satisfy the triangle inequality: if a is the shortest side and c is the longest, then a + b > c .
Write these facts using k as twice the area, and h the altitude to the middle side b.
J. Chris Fisher
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.