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In triangle $ABC,$ $AB = 15,$ $BC = 10,$ and $AC = 12.$ Find the length of the shortest altitude in this triangle.

 Mar 15, 2024
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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

 

 

cool cool cool

 Mar 15, 2024

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