Question

D and E are the points on the sides AB and AC respectively of a ΔABC such that: AD = 8 cm, DB = 12 cm, AE = 6 cm and CE = 9 cm. Prove that BC = 5/2 DE.

Answer 1

We have,

`"AD"/"DB"=8/12=2/3`

And, `"AE"/"EC"=6/9=2/3`

Since, `"AD"/"DB"="AE"/"EC"`

Then, by converse of basic proportionality theorem

DE || BC

In ΔADE and ΔABC

∠A = ∠A                              [Common]

∠ADE = ∠B                           [Corresponding angles]

Then, ΔADE ~ ΔABC              [By AA similarity]

`therefore"AD"/"AB"="DE"/"BC"`                   [Corresponding parts of similar Δ are proportional]

`rArr8/20="DE"/"BC"`

`rArr2/5="DE"/"BC"`

`"BC"=5/2" DE"`