AB=6
Explanation
Step 1
set the equations
due to lengths AD and DC are the same, and the distance DB is common for triangels ADB and DBC
we can state that
triiangles are similar,so
[tex]AB=AC\Rightarrow equation(1)[/tex]
and
[tex]\begin{gathered} AC=12 \\ AC=AB+BC \\ AB+BC=12\Rightarrow equation(2) \end{gathered}[/tex]
Step 2
solve for AB
a) replace the AB value from equation(1) into equation(2)
[tex]\begin{gathered} AB+BC=12\Rightarrow equation(2) \\ AB+AB=12 \\ \text{add like terms} \\ 2(AB)=12 \\ \text{divide both sides by 2} \\ \frac{2(AB)}{2}=\frac{12}{2} \\ AB=6 \end{gathered}[/tex]
therefore, the answer is
AB=6
I hope this helps you
