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Vlad1618 [11]
3 years ago
13

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.

Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

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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