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

 Jul 14, 2024
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Shortest altitude is drawn to  the longest side

 

Area (using Heron's Formula)  = sqrt [ 17 * 2 * 7 * 8 ] =   sqrt [ 1904]

 

[ABC ]   = (1/2) AB * shortest altitude

 

sqrt [ 1904 ] = (1/2) * 15 * shortest altitude

 

sqrt [ 1904 ] / 7.5  =  shortest altitude ≈   5.82

 

 

cool cool cool

 Jul 14, 2024

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