# Triangles - Aptitude Questions and Answers

 In △ABC, the angle bisector of ∠A cuts BC at E. Find length of AC, if lengths of AB, BE and EC are 9 cm, 3.6 cm and 2.4 cm? A) 5.4 cm B) 8 cm C) 4.8 cm D) 6 cm Correct Answer :6 cm Explanation : In △ABC, the angle bisector of ∠A cuts BC at E then according to the angle bisect theorem AB / AC = BE / EC 9 / AC = 3.6 / 2.4 AC = 9*2.4 / 3.6 AC = 6 cm Post/View Answer Post comment Cancel Thanks for your comment.! Write a comment(Click here) ...
 In a triangle, the length of the opposite side of the angle which measures 45° is 8√2 cm, what is the length of the side opposite to the angle which measures 90°? A) 16 cm B) 4√3 cm C) 8√3 cm D) 6√3 cm Correct Answer :16 cm Explanation : △ABC is a right angle triangle ∠B = 90°, ∠C = 45° ∠A = 45° (Angle sum property of △) AB = BC = 8√2 cm By Pythagoras theorem, (AC)2 = (8√2 )2 + (8√2 )2 (AC)2 = 64*2 + 64*2 (AC)2 = 256 AC = 16 cm In the given figure, ∠CAB = 90° and AD⊥BC. If AC = 85 cm, AB = 1.35 m and BC = 2.25m , then AD=? A) 61 cm B) 67 cm C) 57 cm D) 51 cm Correct Answer :51 cm Explanation : In , ∆ BDA ~ ∆ BAC ∠BDA = ∠BAC = 90° ∠B = ∠B (Common) Therefore, AD/AC= AB/BC AD/85 = 1.35/2.25 AD = 85*1.35/2.25 = 51