Answer
AB = 6.3
Explanation
The similar angle shown for the two triangles indicates that both triangles are similar to each other.
Triangle ACD and Triangle ADB are simiar according to the Side-Angle-Side rule of congruence. Hence, we can see that
CD is similar to DB
AC is similar AB
We can write that
[tex]\frac{CD}{AC}=\frac{DB}{AB}[/tex]
CD = 2.5
AC = 5.8
DB = 2.7
AB = ?
[tex]\begin{gathered} \frac{2.5}{5.8}=\frac{2.7}{AB} \\ \text{Cross multiply} \\ 2.5\times AB=2.7\times5.8 \\ \text{Divide both sides by 2.5} \\ \frac{2.5\times AB}{2.5}=\frac{2.7\times5.8}{2.5} \\ AB=6.264 \end{gathered}[/tex]
AB = 6.264 = 6.3 to one decimal place.
Hope this Helps!!!
