SOLUTION: Find the altitude of the longest side of a triangle with sides of 12, 10, and 8.

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Question 388627: Find the altitude of the longest side of a triangle with sides of 12, 10, and 8.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
By Heron's formula, the area of the triangle is

sqrt%2815%2A3%2A5%2A7%29+=+15sqrt%287%29

The altitude of the longest side is the one which is perpendicular to the segment with length 12. Thus,

%281%2F2%29%2812a%29+=+15sqrt%287%29

a+=+%285sqrt%287%29%29%2F2