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Olympiad workbookIOQMProperties of Triangles

The sides of a triangle are x, 2 x+1 and x+2 for some positive rational number x . If one angle of the triangle is 60^ , what is the perimeter of the triangle?

Correct answer

9

Step-by-step solution

x < x+2 < 2 x+1 for existence triangle also triangle is non-equilateral. Hence 60^ = x^2+(2 x+1)^2-(x+2)^2 2 x(2 x+1) x= 3 2 Sides are 3 2 , 7 2 , 4 Perimeter =9

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