Triangles - Aptitude Questions and Answers

View in English View in Hindi

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

Latest Updates

Fill in the blank

I ________ station before the train arrived.

If I ______ a king, I would help everyone.

Radha___________her daughter for an hour.

Errors Identification

Find out which part of the sentence below has an error and mark the option accourdingly -
Sohan was married in 1990 and have three children.

Find out which part of the sentence below has an error and mark the option accourdingly -
There is no money in the bank in Ram Singh's and Rama's joint account.

Direction

Swapnil start from his home and walked 35 km towards east, after that he turned to his right and walked 20 km. He again turned to his right and walks 35 km. Finally, he turned to his left and walked 20 km and reached his office. How far is his office from his home?

Numbers

How many 2 digit numbers are divisible by 6?

HCF and LCM

Find the smallest square number which is exactly divisible by 3, 5, 15, 18, 20 and 24?

HCF and LCM of two numbers are 82 and 574 respectively. if one of the numbers is 287, find the second number?

Numbers

How many numbers between 1200 to 1500 are multiple of 13?

Find the total number of terms in the series : -3, 1, 5, 9,............., 101 ?

Find the sum of the first 20 terms of the series : 8, -3, 11, -6, 14, -12, 17, -24,....... ?

Series

Find the missing term in the given series - 101, 120, 145, 168, (?), 224

Find the missing term in the given series - 11A13, 17E19, (?), 31O37, 41U43

Find the missing term in the given series - 2,4,8,3,9,27,4,16,(?),5,25,125

Agriculture

Which gas is fixed by Rhizobium bacteria present in the root nodules of a pea plant ?

Chemistry

The formation of sulphurous acid involves ?

The acid present in soft drinks is ?