Question

Two sides of a triangle are given by the roots of the equation x^2 − 5 x + 6 = 0 and the angle between them is π /3 . The perimeter of the triangle is

Answer 1

Answer:

= 3√ 3 /2

Step-by-step explanation:

x^2 − 5 x + 6 = 0

x^2 − 3 x - 2x+ 6 = 0

x(x-3)-2(x-3)=0

(x-2)(x-3) = 0

x=2 and 3

Two sides of triangle = 2,3

Area of triangle = 1/2 * 2 * 3 * sin(π /3)  (using area = 1/2 ab sin C)

= 1/2 * 2 * 3 * (√ 3 /2)

= 3√ 3 /2