In a triangle ABC, AB = 9 cm, BC = 40cm, and AC = 41 cm, then the triangle is

The correct answer is A, the triangle is right angled. Check the largest side first. AC = 41 is the longest, so compare AC² with AB² + BC². 41² = 1681, while 9² + 40² = 81 + 1600 = 1681. The two sides are equal, so by the converse of the Pythagoras theorem the angle opposite AC, which is angle B, is exactly 90°.

Why the other options fail:

• B (Obtuse angled): An obtuse triangle needs AC² greater than AB² + BC². Here they are equal, so no angle exceeds 90°.
• C (Acute angled): An acute triangle needs AC² less than AB² + BC². Here they are equal, so the triangle is not acute.
• D (Equal angled): Equiangular triangles are equilateral, with all angles 60°. The sides here are 9, 40 and 41, all unequal, so this is impossible.

The core concept is the converse of the Pythagoras theorem and the side-square classification of triangles. It is a basic geometry skill in Prelims, and in Mains it sits behind surveying and construction, where right angles are checked using 3-4-5 style triples.

Trap: Aspirants often see that no two sides are equal and pick acute, or read 9, 40, 41 as an unfamiliar set and guess. Always compare the square of the longest side with the sum of the other two squares.