DES A 38 en given figure LABC = LDA AB = 8cm, AC=4cm, AD=5cm Prove that ACD is similar to BCA and find B

Question

DES
A
38 en given figure LABC = LDA
AB = 8cm, AC=4cm, AD=5cm
Prove that ACD is similar to
BCA
and find
BC and CD​

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Vivian 3 weeks 2021-08-19T10:03:56+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-19T10:05:33+00:00

    Answer:AB = 8 cm,


    AC = 4 cm, AD = 5 cm.


    (i) In ΔACD and ΔBCA


    ∠ABC = ∠DAC (Given)


    ∠ACD = ∠BCA      (Common)


    ⇒ ΔACD ~ ΔBCA   (AA axiom).


    Hence  ΔACD is similar to ΔBCA.


    Hence proved.


    (ii) As we have,


    AC/BC = CD/CA = AD/BA


    ⇒ 4/BC = CD/4 = 5/8


    ⇒ 4/BC = 5/8


    ⇒ BC = 8 × 4/5 = 32/5


    = 6.4 cm.


    And  CD/4 = 5/8


    ⇒ CD = 5 × 4/8


    ⇒ CD = 2.5 cm.


    (iii) Area of ΔACD/Area of ΔABC = (AC/AB)2


    = (4/8)2


    = ¼


    Thus area of ΔACD : area of ΔABC = 1 : 4.

    Step-by-step explanation:

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