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IgorC
9 days 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:
Inessa [12.2K]9 days ago
8 0

Let G represent the intersection of EF & BC.

According to 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

The height of △AED = EF

Thus, EF = EG + GF = 1.5 + 3 = 4.5

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