Triangles ABC and DEF are similar, which means corresponding sides are proportional to one another. Here, side AB corresponds to DE, BC to EF, and AC to DF.
We know the length of AB and AC, and we can figure out the length of BC using the Pythagorean theorem:
[tex]8^2+BC^2=17^2\implies BC=15[/tex]
Sides BC and EF correspond to one another, and EF is 2 times longer than BC. This means DF is 2 times longer than 17, so that [tex]x=34[/tex].
