 # 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]

11 years ago

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

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

11 years ago

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