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In triangle $ABC,$ $AB = 10,$ $BC = 24,$ and $AC = 26.$ Find the length of the shortest altitude in this triangle.

 Apr 25, 2020
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Since 102 + 242 =  262, this is a right triangle with angle(B) the right angle.

The shortest altitude will be the one from angle(B).

Call the point where this altitude hits side(AC) "X".

AX/AB  =  AB/AC     --->     AX/10  =  10/26     --->     AX  =  50/13.

Triangle(ABX is a right triangle:  (50/13)2 + (BX)2  =  102     --->     (BX)2  =  14400/169     --->   BX  =  120/13.

 Apr 25, 2020

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