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:

$\frac{eg}{ef} = \frac{bc}{ad}$

and EF= EG+GF=EG+3

$\frac{eg}{eg + 3} = \frac{7}{21}$

$21eg = 7eg + 21$

$14eg = 21$

$eg = \frac{21}{14} = \frac{3}{2} = 1.5$

length of the altitude of △AED=EF

EF=EG+GF=1.5+3=4.5