Answer:
[tex]AB=\dfrac{38}{3}\ units[/tex]
Step-by-step explanation:
ABCD is a rhombus, then
[tex]AB=BC=CD=DA[/tex]
Since
[tex]BC=2x+8\\ \\CD=5x+1,[/tex]
then
[tex]BC=CD\Rightarrow 2x+8=5x+1[/tex]
Solve this equation:
[tex]2x-5x=1-8\\ \\-3x=-7\\ \\3x=7\\ \\x=\dfrac{7}{3}[/tex]
Then
[tex]BC=2\cdot \dfrac{7}{3}+8=\dfrac{14}{3}+8=\dfrac{14+8\cdot 3}{3}=\dfrac{14+24}{3}=\dfrac{38}{3}\ units[/tex]
Therefore,
[tex]AB=\dfrac{38}{3}\ units[/tex]
