Mathematics: 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.

I believe the answer would be $79.50....

The extensions of the legs ab and cd of a trapezoid

detrickboucicaut

12.01.2022

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

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