PrepRung
Sign inSign up free

NDA 2017 Maths · Mathematics · Properties of Triangles · medium

For a triangle with sides a,b,c, consider the statements. 1. If a^2+b^2<c^2, then angle C is obtuse. 2. If a:b:c=1:√3:2, then the triangle is…

Single correct option

For a triangle with sides a,b,ca,b,c, consider the statements.

1. If a2+b2<c2a^2+b^2<c^2, then angle CC is obtuse.
2. If a:b:c=1:3:2a:b:c=1:\sqrt3:2, then the triangle is right-angled.

Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (C) Both 1 and 2

By the cosine rule cos⁡C=a2+b2−c22ab<0\cos C=\frac{a^2+b^2-c^2}{2ab}<0 when a2+b2<c2a^2+b^2<c^2, so CC is obtuse. For sides 1,3,21,\sqrt3,2: 1+3=41+3=4, so the Pythagoras relation holds and the triangle is right-angled. Both are correct.
Report a mistake

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake