In triangle $ABC,$ $AB = 15,$ $BC = 10,$ and $AC = 12.$ Find the length of the shortest altitude in this triangle.
Semi-perimeter = [ 15 + 12 + 10 ] / 2 = 18.5
Area = sqrt [ 18.5 (3.5) (6.5)(8.5) ]
Shortest altitude drawn to the longest side
sqrt [18.5 (3.5)(6.5)(8.5)] = (1/2) 15 * altitude
Altitude = sqrt [ 18.5(3.5)(6.5)(8.5) ] / 7.5 ≈ 7.97
+1167 
