Question

why EF is taken as the height of ∆BDE if it is already the height of ∆FEB?​

Answer 1

Answer:

I will not ask you to specify the exact EF.

Answer 2

It is the height of both the triangles, BDE as well as FEB.
Since BDE is an obtuse-angled triangle, it’s perpendicular/height is outside the triangle.
In order to prove the theorem, this step is reqd.
Hope this helps u :)