KVPY SA Exam 2013 Question Paper

Question : 3 of 80

Marks: +1, -0

The number of values of b for which there is an isosceles triangle with sides of lengths b + 5 ,3b - 2 and 6 - b is

Solution:

Case (I)
b + 5 = 3b - 2
⇒ b =

7/2

So sides are

17/2,17/2,5/2

Case (II)
b + 5 = 6 - b = b =

1/2

Sides

11/2,-1/2,11/2

Not possible
Case (III)
3b - 2 = 6 - b
4b = 8
b = 2
7, 4, 4
two cases are possible

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