Question

In ΔABC, DE is parallel to BC and DE = 3:8.

Find:
(i) AD : BD
(ii) AE, if AC = 16.

Answer 1

(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.