Question

The extensions of the legs AB and CD of a trapezoid ABCD intersect at point E. Find the lengths of the altitude of △AED drawn to the base AD, if BC=7cm, AD=21cm, and the length of an altitude of a trapezoid is 3cm.

Answer 1

let's call G the intersection point of EF & BC.

according to the thales' theorem:

`(eg)/(ef) = (bc)/(ad)`

and EF= EG+GF=EG+3

`(eg)/(eg + 3) = (7)/(21)`

`21eg = 7eg + 21`

`14eg = 21`

`eg = (21)/(14) = (3)/(2) = 1.5`

length of the altitude of △AED=EF

EF=EG+GF=1.5+3=4.5