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Question

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides are

A
6,7,8
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B
4,5,6
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C
1,2,3
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D
3,4,5
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Solution

The correct option is B 4,5,6
Let the sides of triangle are x1,x,x+1
From sine rule
sinAA=sinBB=sinCC
sinθx1=sin2θx+1
sinθx1=2sinθcosθx+1
x+12cosθ(x1)=0...(1)
By cosine rule
cosθ=(x+1)2+x2(x1)22x(x+1)
cosθ=x+42(x+1)...(2)
From (1) and (2)
x+12(x+42(x+1))(x1)=0
x=5
Hence, sides of triangle are 4,5,6

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