MathematicsIn figure, ∠ ABC=90° and BD⊥AC if BD = 8cm and AD =4cm, Find CD.

In figure, ∠ ABC=90° and BD⊥AC if BD = 8cm and AD =4cm, Find CD.


969179

  1. A
    41 cm
  2. B
    16 cm
  3. C
    19 cm
  4. D
    22 cm 

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given is a figure,
    969179∠ABC= 90° and   BD⊥AC.
    BD = 8 cm and AD = 4 cm
    In ΔDBA and ΔDCB,
    ∠D = ∠D (Right angles)
    ∠DBA = ∠DCB (∵ ∠DBA = 90° - ∠A, ∠DCB = 90° - ∠A,)
    ∠DAB = ∠DBC (If two angles of triangles are equal then third angle is also equal)
    ΔDAB ~ ΔDBC…….(1) (By AAA similarity criteria)
    Apply the similar triangle property that sides are proportional to equation (1),
    ADBD=BDCD…………(2)(∵ΔDAB ~ ΔDBC)
    Substitute given values of BD = 8 cm and AD = 4 cm  in equation (2),
    ⇒48=8CD ⇒CD=8×84 ⇒CD=16 Thus, the value of CD is 16 cm.
    Therefore, option 2 is correct.
     
    Chat on WhatsApp Call Infinity Learn