Question

A line segment DE is drawn parallel to base BC of ΔABC which cuts AB at point D and AC at point E. If AB = 5BD and EC = 3.2 cm, find the length of AE.

Answer 1

In ΔABC

DE || BC

AB = 5BD, EC = 3.2 cm

To find AE

Since, DE || BC

∴ ΔADE ∼ ΔABC

Since a line drawn parallel to one side of triangle divides the other sides proportionality.

∴ `(AD)/(AB) = (AE)/(EC)`  ...`{{:(∵ (AB)/(BD) = 5/1),(\implies (BD)/(AB) = 1/5),(AD = AB - BD = 5 - 1 = 4),(∴ (AD)/(DB) = 4/1):}}`

`\implies 4/1 = (AE)/3.2`

`\implies AE = (4 xx 3.2)/1`

= `12.8/1`

= 12.8 cm