Triangle BCD is similar to triangle ACE, so corresponding side lengths are proportional to one another and we have
[tex]\dfrac34=\dfrac{5.2}{5.2+x}[/tex]
Solve for [tex]x[/tex]:
[tex]3(5.2+x)=4\cdot5.2\implies15.6+3x=20.8\implies3x=5.2\implies x\approx1.73[/tex]
