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Question
In ΔABC, DE is parallel to BC and DE = 3:8.
Find:
(i) AD : BD
(ii) AE, if AC = 16.
Solution
(i) Since DE ||BC
`"DE"/"BC" = "AD"/"AB"`
⇒ `(3)/(8) = "AD"/"AB"`
⇒ `"AD"/"AB" = (3)/(8)`
Since DB = AB - AD
⇒ DB
= 8 - 3
= 5
Therefore,
AD : DB = 3 : 5
(ii) DE : BC = 3 : 8
Since DE || BC
`"DE"/"BC" = "AE"/"AC"`
⇒ `(3)/(8) = "AE"/(16)`
⇒ AE = `(3 xx 16)/(8)`
⇒ AE = 6.
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