Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

Olympiad workbook

Exam: Olympiad workbook
Subject: IOQM
Chapter: Properties of Triangles

Olympiad workbook · IOQM · Properties of Triangles

The sides of a triangle are x, 2 x+1 and x+2 for some positive...

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^{\circ}

, 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

\cos 60^{\circ}=\frac{x^2+(2 x+1)^2-(x+2)^2}{2 x(2 x+1)}

\Rightarrow x=\frac{3}{2}

\therefore \quad

Sides are

\frac{3}{2}, \frac{7}{2}, 4

\Rightarrow

Perimeter

=9

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

The incircle Γ of a scalene triangle A B C touches B C at D, C A at E and A B at F . Let… Olympiad workbook The sides x and y of a scalene triangle satisfy x+(2 Δ)/(x)=y+(2 Δ)/(y) , where Δ is the… Olympiad workbook In a triangle A B C , the median A D divides ∠ B A C in the ratio 1: 2 . Extend A D to E… Olympiad workbook Let A B C be a triangle let D be a point on the segment B C such that A D=B C . Suppose ∠… Olympiad workbook Two sides of a regular polygon with n sides, when extended, meet at an angle of 28^ ∘ .… Olympiad workbook Let A B C be an isosceles triangle with A B=A C and incentre I . If A I=3 and the… Olympiad workbook Let A B C be an acute-angled triangle and P be a point in its interior. Let P_A, P_B… Olympiad workbook Let A B C be a triangle with ∠ B A C=90^ ∘ and D be the point on the side B C such that A… Olympiad workbook Full Properties of Triangles list All Olympiad workbook PYQs