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aditya kulkarni Grade: 11
        

In a triangle if the lenght of the sides are a,b,c.then the given condition is a2+b2+c2=ab+bc+ca.then the triangle formed is a]right angled b]obtuse angled c]acute angled........[I want to know  about the angle of the triangle ...so please help me to solve this problem]


 

6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

a2+b2+c2 = ab+bc+ac               (given)


cosA = b2+c2-a2/2bc


2bccosA = b2+c2-a2           ...........1


2accosB = a2+c2-b2             ..........2


2abcosC = a2+b2-c2            .........3


adding 1,2,3


2(abcosC+bccosA+accosB) = a2+b2+c2       ........4


a2+b2+c2 = ab+bc+ac              (given)


so , 2(abcosC+bccosA+accosB) = ab+bc+ac


      2ab(cosC-1/2) + 2bc(cosA-1/2) + 2ac(cosB-1/2) = 0


from this eq , cosC = cosA = cosB = 1/2


A=B=C = Pi/3


so the triangle is equilateral , acute angled triangle...


approve if u like my ans

6 years ago
Supreeth Gadamsetty
4 Points
										

though this isnt the exact solution but if you are looking for answer directly


the above condition satisifies when a=b=c,so it can be equilateral corresponds to the answer acute angled

6 years ago
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