Question

In the following figure, DE || BC and `(AD)/(DB) = 3/4`. If AC = 8.4 cm, find EC.

Answer 1

Since DE || BC, triangles △ADE and △ABC are similar.

So, `(AD)/(AB) = (AE)/(AC)`

Given: `(AD)/(DB) = 3/4`

Thus,

AB = AD + DB

So the ratio:

AD : AB = 3 : (3 + 4)

∴ AD : AB = 3 : 7

Hence, `(AE)/(AC) = 3/7`

Given: AC = 8.4 cm,

`AE = 3/7 xx 8.4`

∴ AE = 3.6 cm

Now,

EC = AC − AE

EC = 8.4 − 3.6

∴ EC = 4.8 cm