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CAT 2000 — QA Question 46

Basics of TrianglesEasy

If a, b, c are the sides of a triangle, and a2 + b2 + c2 = bc + ca + ab, then the triangle is

Answer & solution

Correct answer: equilateral

  • equilateral

  • B

    isosceles

  • C

    right angled

  • D

    obtuse angled

Solution

a, b, c are the sides of a triangle.

It is given that a2 + b2 + c2 = bc + ca + ab

⇒ a2 + b2 + c2 - bc - ca - ab = 0

⇒ 2a2 + 2b2 + 2c2 - 2bc - 2ca - 2ab = 0

⇒ (a2 -2ab + b2) + (b2 - 2bc + c2) + (c2 - 2ca + a2) = 0

⇒ (a - b)2 + (b - c)2 + (c - a)2 = 0

This is possible only if a = b = c

i.e., the triangle is equilateral.

Hence, option (a).

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CAT 2000 QA Q46: If a, b, c are the sides of a triangle, and a 2 + b 2 + c 2 = bc + ca + ab, then the triangle is — Solution | TheCATExam