A) \[\frac{1}{26}\]
B) \[\frac{1}{27}\]
C) \[\frac{1}{21}\]
D) \[\frac{1}{15}\]
Correct Answer: B
Solution :
Required probability\[=\frac{1}{27}\] NOTE: Don?t consider equilateral triangle Consider only 21 cases of isosceles triangle, each case occurring thrice \[(2,2,1)(2,2,3)(3,3,1)(3,3,2)(3,3,4)(3,3,5)(4,4,1)\]\[(4,4,2)(4,4,3)(4,4,5)(4,4,6)(5,5,1)(5,5,2)(5,5,3)\]\[(5,5,4)(5,5,6)(6,6,1)(6,6,2)(6,6,3)(6,6,4)(6,6,5)\]Out of which \[(6,6,5)\]has maximum area. Hence required probability is\[\frac{3}{63}=\frac{1}{21}\] NOTE: If we consider equilateral triangle, there are \[21\times 3=63\]occurrences of non-equilateral isosceles triangles and 6 occurrences of equilateral triangle out of which \[(6,6,6)\]has maximum area. So the required probability would have been\[\frac{1}{69}\]and not\[\frac{1}{27}.\]
You need to login to perform this action.
You will be redirected in
3 sec
