# Triangles - Aptitude Questions and Answers

 ABC is a triangle and D is a point on the side BC. If BC =12 cm, BD = 9 cm and ∠ADC = ∠BAC, then the length of AC is equal to? A) 5 cm B) 6 cm C) 8 cm D) 9 cm Correct Answer : 6 cm Explanation : In ΔBAC and ΔADC ∠ADC = ∠BAC (Given) ∠ACB = ∠DCA (Common angle) ΔBAC ~ ΔADC (AA similarity criteria) The ratio of sides is also equal. AC/DC = BC/AC AC*AC = BC*DC AC2 = 12*3 ( BC= BD+CD =12 ) AC2 = 36 AC = 6 cm Post/View Answer Post comment Cancel Thanks for your comment.! Write a comment(Click here) ...
 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 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