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Two sides of a triangle are given by the roots of the equation x^2-5x+6=0 and angle between the sides is 60°.then the perimeter of the triangle is

Two sides of a triangle are given by the roots of the equation x^2-5x+6=0 and angle between the sides is 60°.then the perimeter of the triangle is
 

Grade:12

2 Answers

Arun
25750 Points
4 years ago
On Solving quadratic equations, we get x = 3 and 2
 
Hence sides are 3 and 2
 
Now
 
Cos 60 = 3² + 2² - c² /(2*3*2)
 
1/2 = 13 -c² /12
 
6 = 13 -c²
 
c² = 7
Hence c = √7
 
Now perimeter = 2 +3 + √7 = 5 + √7
 
Hope it helps
 
Thanks and regards
Vikas TU
14149 Points
3 years ago
Dear student 
x^2-5x+6=0 x^2-2x-3x+6=0
x(x-2)-3(x-2)=0 (x-3)(x-2)=0
x=2,3
Let the sides of the triangle be named as a,b,c where a=2, b=3 and c=?
To the find the value of c: Given that angle between two sides is 60° By using cosine rule CosC=a^2+b^2-c^2/2ab 1/2=4+9-c^3/2*2*
3 c=7^1/2
then perimeter of the triangle ABC =a+b+c=2+3+7^1/2 =5+7^1/2

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