AP EAMCET · Maths · Properties of Triangles
Two sides of a triangle are given by the roots of the equation \(x^2-5 x+6=0\) and the angle between the sides is \(\frac{\pi}{3}\). Then, the perimeter of the triangle is
- A \(5+\sqrt{2}\)
- B \(5+\sqrt{3}\)
- C \(5+\sqrt{5}\)
- D \(5+\sqrt{7}\)
Answer & Solution
Correct Answer
(D) \(5+\sqrt{7}\)
Step-by-step Solution
Detailed explanation
Given equation is \(\begin{aligned} x^2-5 x+6 & =0 \\ \Rightarrow(x-3)(x-2)=0 \Rightarrow x & =3,2 \end{aligned}\) These are the sides of a triangle Let \(a=3, b=2, \angle C=\frac{\pi}{3}\)…
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