"Twin peaks" math quesiton

[mpereiraluppi]

Hi,

I was reviewing my results for a practice test and I got confused with
the explanation:

the question is: "Twin peaks"

my question is:
why do you assume that AE is equal to ED, and that E is the midpoint
of segment BC if the figure is not drawn to scale? As far as I know,
BE could be different than EC.

Thanks!

[tommywallach]

The explanation doesn't assume that. As you said, we can't know that for sure. What we CAN know is that any right triangle implies a second right triangle of equal area that "turns" it into a rectangle. Look at triangle ABE. If you draw a point directly DOWN from point E (on the line AD) and call it F, you can see that AFE = ABE. By the same argument, triangle EFD = CDE. Therefore, if ABE + CDE = 24, then AFE + EFD must also equal 24.

-t