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
Answers
Answered by
13
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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