Focus on triangles DFC and DFE. They are both right triangles, and they share the side DF. Moreover, we have DE=DC.
So, the two triangles are congruent, because they are two right triangles with the same hypotenuse and a common leg.
So, the other legs must be equal as well, and we have
[tex]3x+15=8x \iff 5x=15 \iff x=3[/tex]
which implies
[tex]EF=3x+15=3\cdot 3+15 = 9+15=24[/tex]
