Math CentralQuandaries & 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.


You need two facts here:

  1. base times altitude equals twice the area of a triangle, and
  2. 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

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