ΔABC and ΔDBE are similar. Therefore the side are in proportion:
[tex]\dfrac{DE}{DB}=\dfrac{AC}{AB}[/tex]
DE = 3x - 5
DB = a
AC = 20
AB = a + a = 2a
Substitute:
[tex]\dfrac{3x-5}{a}=\dfrac{20}{2a}[/tex] cross multiply
[tex]2a(3x-5)=20a[/tex] divide both sides by 2a ≠ 0
[tex]3x-5=10[/tex] add 5 to both sides
[tex]3x=25[/tex] divide both sides by 3
[tex]x=\dfrac{25}{3}[/tex]
[tex]\boxed{x=8.\overline{3}}[/tex]
