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Aptitude miscellaneous
  1. If the bisector of an angle of Δ bisects the opposite side, then the Δ is :










  1. View Hint View Answer Discuss in Forum

    According to given question, ∠1 = ∠2

    ∴AB = BD
    ACAD


    Correct Option: B

    Since ∠1 = ∠2

    ∴AB = BD
    ACAD

    But BD = CD (given)
    ∴AB = 1
    AC

    AB = AC
    ∴ the given ∆ is isosceles


  1. The areas of two similar Δs are 81 cm2 and 144 cm2. If the largest side of the smaller Δ is 27 cm, then the largest side of the larger Δ is :












  1. View Hint View Answer Discuss in Forum

    Let ABC and DEF be the two similar Δs having area 81 cm2 and 144 cm2 respectively:
    Let BC = 27 cm
    Then since ΔABC ∼ ΔDEF

    ∴area (∆ABC) = BC2(area Theorem)
    area (∆DEF)EF2

    Correct Option: C

    Let ABC and DEF be the two similar Δs having area 81 cm2 and 144 cm2 respectively:
    Let BC = 27 cm
    Then since ΔABC ∼ ΔDEF

    ∴ar (∆ABC) = BC2(area Theorem)
    ar(∆DEF)EF2

    81 = (27)2⇒9 = 27
    144x212x

    ∴ x = 36 cm.

  1. In the given figure ∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm. Find BC.












  1. View Hint View Answer Discuss in Forum

    According to question, Given that
    ∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm
    In ΔABC, AD is the bisector of ∠A

    AB=BD(Internal bisector prop.)
    ACCD

    Correct Option: A

    According to question, Given that
    ∠BAD = ∠CAD. AB = 4 cm, AC = 5.2 cm, BD = 3 cm
    In ΔABC, AD is the bisector of ∠A

    AB=BD(Internal bisector prop.)
    ACCD

    4=3⇒ DC = 3.9 cm
    5.2DC

    But BC = BD + CD = 3cm + 3.9 cm = 6.9 cm

  1. A ladder 15 m long reaches a window which is 9 m above the ground on one side of street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. What is the width of the street:










  1. View Hint View Answer Discuss in Forum

    Draw a figure as per given question,
    In a Right triangle ADC, Use the (Pythagoras Theorem)
    AC = √DC2 - AD2

    In a Right triangle BCE, Use the (Pythagoras Theorem)
    CB = √ CD2 - BE2



    Correct Option: D

    Draw a figure as per given question,
    In a Right triangle ADC, Use the (Pythagoras Theorem)
    AC = √DC2 - AD2
    ⇒ AC = √ 152 - 9 2
    ⇒ AC = √ 225 - 81
    ⇒ AC = √ 144
    ⇒ AC = 12 cm
    In a Right triangle BCE, Use the formula
    CB = √ CD2 - BE2
    ⇒ CB = √15 2 - 122
    ⇒ CB = √225 - 144
    ⇒ CB = √ 81
    ⇒ CB = 9 m

    ∴ Width of the street (AC + BC) = AB = 12 + 9 = 21 m.


  1. D and E are the points on the sides AB and AC respectively of ΔABC such that AD = 8 cm, BD = 12 cm, AE = 6 cm and EC = 9 cm. Then find BC/ DE.












  1. View Hint View Answer Discuss in Forum

    SinceAD=AE=2
    DBEC3

    ∴ DE || BC (by converse of BPT)
    ∴ ΔADE ∼ ΔABC (AA similarity)

    Correct Option: A

    SinceAD=AE=2
    DBEC3

    ∴ DE || BC (by converse of BPT)
    ∴ ΔADE ∼ ΔABC (AA similarity)
    AD=DE
    ABBC

    8=DE
    ABBC

    2=DE⇒BC=5
    5BCDE2