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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.

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 BC7cm AD21cm and t class=

Respuesta :

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

according to the thales' theorem:

[tex] \frac{eg}{ef} = \frac{bc}{ad} [/tex]

and EF= EG+GF=EG+3

[tex] \frac{eg}{eg + 3} = \frac{7}{21} [/tex]

[tex]21eg = 7eg + 21[/tex]

[tex]14eg = 21[/tex]

[tex]eg = \frac{21}{14} = \frac{3}{2} = 1.5[/tex]

length of the altitude of △AED=EF

EF=EG+GF=1.5+3=4.5

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