OE


Given that, ABC is an obtuse angled triangle, where AC is the longest side and AB is the
shortest side.
In a triangle,
(Difference of other two sides) < Any side of the triangle < (Sum of other two sides)
So,
3k – k < 10 < 3k + k
2k < 10 < 4k
Therefore, 2k < 10 and 10 < 4k
that is, k < 5 and 2.5 < k
Therefore, k lies between 2.5 and 5.
It is given that k is an integer,
Therefore, K can be 3 or 4.
If k = 3,

AC = 3k = 9
But it is given that AC is longest side
Hence, k cannot be 3.
If k = 4,
AB = 4 and AC = 3k = 12
This satisfies the statements given in the question.
The only value of k possible is 4.
Ans. (B)