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If the sides of a triangle are 17 , 25a ...

If the sides of a triangle are `17 , 25a n d28 ,` then find the greatest length of the altitude.

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We know from geometry that the greatest altitude perpendicular to the shortest side
Let `a = 17, b = 25`
and `c = 28`
Now, `Delta = (1)/(2) AD xx BC`
or `AD = (2Delta)/(17)`
where `Delta^(2) = s(s -a) (s -b) (s-c)`
`= 210^(2)`
`rArr AD = (420)/(17)`
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