Answer to one mathleague quesiton from AoPS

Question is here.

You have two congruent triangles. 17-same angle and- x (SAS)
Using distance formula, the two green lines are of the same length.
${(a-25)}^2+{(20-15)}^2=a^2+{20}^2$
a = 5

Use another distance formula to get x -- the blue line.
$\sqrt{{(5-17)}^2+{20}^2}=\sqrt{544}=4\sqrt{34}$