Length of the sides of a triangle are a, b and c. If a2 + b2 + c2 = ab + bc + ca, then the triangle is
Explanation:
Given, a2 + b2 + c2 = ab + bc + ca
⇒ 2a2 + 2b2 + 2c2 = 2ab + 2bc + 2ca
⇒ 2a2 + 2b2 + 2c2 - 2ab - 2bc - 2ca = 0
⇒ (a2 - 2ab + b2) + (c2 - 2ac + a2) (b2 - 2bc + c2) = 0
⇒ (a - b)2 + (a - c)2 + (b - c)2 = 0
This is only possible when a = b = c
∴ The given triangle is an equilateral triangle.
Hence, option (c).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.