Answer:
To figure out the length of AB, we will calculate the length of BC first
Step 1:
Calculate length BC
Using the Pythagoras theorem, we will have that
[tex]\begin{gathered} BC^2=BD^2+CD^2 \\ BC^2=3^2+4^2 \\ BC^2==9+16 \\ BC^2=25 \\ BC=\sqrt{25} \\ BC=5 \end{gathered}[/tex]
Step 2:
Calculate the length of segment AB
Using the Pythagoras theorem, we will have
[tex]\begin{gathered} AB^2=AC^2+BC^2 \\ AB^2=12^2+5^2 \\ AB^2=122+25 \\ AB^2=169 \\ AB=\sqrt{169} \end{gathered}[/tex]
Hence,
The final asnwer is
[tex]\Rightarrow\sqrt{169}[/tex]
OPTION D is the right answer
