Question

Which one of the following is correct if a, b and c are the sides of a triangle ABC and \(\begin{vmatrix}a^2 & b^2 & c^2 \\(a + 1)^2 & (b + 1)^2 & (c + 1)^2 \\ (a – 1)^2 & (b – 1)^2 & (c – 1)^2 \end {vmatrix}\) ?

(a) ABC is an equilateral triangle

(b) ABC is an isosceles triangle

(c) ABC is a right angled triangle

(d) ABC is a scalene triangle

The question was asked in an internship interview.

My doubt stems from Application of Determinants in division Determinants of Mathematics – Class 12

Answer 1

Correct option is (b) ABC is an isosceles triangle

Explanation: When a = b or b = c or c = a the determinant reduces to 0

It is not necessary that a = b = c for determinant to be 0

Therefore, the triangle is isosceles.