Quant Question Of The Day: 248
If 2 altitudes in a triangle are 6 and 10 , then what is the maximum possible integer length of the third altitude of the triangle
- 12
- 14
- 15
- 10
If 2 altitudes in a triangle are 6 and 10 , then what is the maximum possible integer length of the third altitude of the triangle
Answer: (2) 14 Solution let’s say 3 altitudes are h1, h2, h3 then area (A) = (ah1)/2 = (bh2)/2 = (ch3)/2 now a=A/ h1; b=A/h2 ; c=A/h3 now inequality of sides a-b<c<a+b so (1/h1- 1/h2) < 1/h3< (1/h1+1/h2) so 3.75<h3<15 so maximum integer value = 14
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