Triangles - Aptitude Questions and Answers

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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

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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

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