SMO 2017 Junior Round 1 Question 6

Question 6

Let $ABCD$ be a rectangular sheet of paper with $AB=6$ and $BC=8$. We can fold the paper along the crease line $EF$ so that point $C$ coincides with point $A$. Find the length of the resulting line segment $AF$.

Question illustration

$\frac{25}4$
$\frac{13}2$
$\frac{27}4$
$7$
None of the above