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

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

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

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