Question

What is the length of x? What is the length of EF? Only enter numbers in the answer boxes below:

Answer 1

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

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

And since x=3, the length of EF is

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