SOLUTION: The area of a triangle,the length of whose altitudes are 5, 12 and 13 units, is- a)30 sq units b)60 sq units c)78 sq units d)such a triangle does not exist.

Question 510547: The area of a triangle,the length of whose altitudes are 5, 12 and 13 units, is-
a)30 sq units
b)60 sq units
c)78 sq units
d)such a triangle does not exist.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Such a triangle would have an area of

where s1, s2, s3 are the side lengths of the triangle. Hence,

We can let s1 = 156k, s2 = 65k and s3 = 60k for some positive number k. It is apparent that such a triangle does not exist because 60k + 65k < 156k (it violates the triangle inequality), so the answer is D, such a triangle does not exist.
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