Focus on triangles DFC and DFE:
- They are both right triangles because DF is perpendicular to EC
- DC=DE
- DF is a common side
So, the two triangles are congruent. It follows that CF=FE, and in particular
[tex]8x=3x+15 \iff 5x=15 \iff x=3[/tex]
And since x=3, the length of EF is
[tex]EF=3x+15=3\cdot 3+15=24[/tex]
