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Question

In ΔABC, DE ∥ BC. If AD = 3 cm, DB = 2 cm and DE = 6 cm, then BC = ?


(a) 9 cm
(b) 10 cm
(c) 12 cm
(d) 18 cm

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Solution

(b) 10 cm
In Δ ABC, DE ∥ BC. Then,
ADDB=AEEC ( By Thales' theorem)
BDAD=ECAE
BDAD+1=ECAE+1
BD+ADAD=EC+AEAE
ABAD=ACAE (Since BD + AD = AB and EC + AE = AC)
and A=A (Common)
ABC~ADE (SAS similarity)
Thus,
ABAD=BCDE [In similar triangles, corresponding sides are similar]
53=BC6
BC=6×53=10 cm

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