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The number of values of b for which there is an isosceles triangle with sides of length b + 5, 3b – 2 and 6 – b is 1. 0 2. 2 3. 1 4. 3
putting different values,when b=2property of isosceles triangle is proved.
Case (I) b + 5 = 3b - 2 => b = 7/2 So sides are 5/2 , 17/2 , 17/2 Case (II) b + 5 = 6 - b = b = 1/2 Sides 11/2 , -1/2 , 11/2 is Not possible Case (III) 3b - 2 = 6 - b 4b = 8 b = 2 7, 4, 4 two cases are possibletherefore answer is 2
Case (I) b + 5 = 3b - 2 => b = 7/2 So sides are 5/2 , 17/2 , 17/2 Case (II) b + 5 = 6 - b = b = 1/2 Sides 11/2 , -1/2 , 11/2 is Not possible Case (III) 3b - 2 = 6 - b 4b = 8 b = 2 7, 4, 4 two cases are possibletherefore answer is 2.
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