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

 Dec 14, 2023
 #1
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The shortest altitude will be drawn to the longest side

 

Using Heron's formula, the semi-perimeter  =  [ 9 + 10 + 15 ] /  2     =  17 

 

The area =     sqrt [ 17 * (17 - 9) * (17 -10) * (17 -15) ] =  sqrt [ 17 * 8 * 7 * 2 ]  =

 

sqrt [ 1904]

 

So  area  =  (1/2) (AB) (altitude drawn to AB)

 

sqrt [ 1904]  = (1/2)(15) ( altitude drawn to AB)

 

sqrt [ 1904] / 7.5  = altitude drawn to AB  ≈  5.82 

 

cool cool cool

 Dec 15, 2023

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