Question

Can anyone help me with this?

Answer 1

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

$3x+15=8x \iff 5x=15 \iff x=3$

which implies

$EF=3x+15=3\cdot 3+15 = 9+15=24$