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In triangle $ABC,$ $AB = 15,$ $BC = 9,$ and $AC = 10.$ Find the length of the shortest altitude in this triangle.

 Apr 30, 2024
 #1
avatar+128772 
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Semi-perimeter  =  [ 15 + 9 + 10 ] /  2  =  17

 

Area  =   sqrt [ 17 * 2 * 7 * 8 ]  = 4 sqrt 119

 

Shortest altitude is  drawn  to the longest side

 

4 sart 119 =  (1/2) AB * Altityude

 

4 sqrt 119 = (1/2) 15 * Altitude

 

[ 4 sqrt 119  ]  /  [ 1/2 * 15 ]  =   [8 sqrt 119] / 15 =  Altitude  ≈  5.82

 

cool cool cool

 Apr 30, 2024

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