Question

Find the length of the segment AB.A. √50B. √19C. √144D. √169

Answer 1

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

`\begin{gathered} BC^2=BD^2+CD^2 \\ BC^2=3^2+4^2 \\ BC^2==9+16 \\ BC^2=25 \\ BC=√(25) \\ BC=5 \end{gathered}`

Step 2:

Calculate the length of segment AB

Using the Pythagoras theorem, we will have

`\begin{gathered} AB^2=AC^2+BC^2 \\ AB^2=12^2+5^2 \\ AB^2=122+25 \\ AB^2=169 \\ AB=√(169) \end{gathered}`

Hence,

The final asnwer is

`\Rightarrow√(169)`

OPTION D is the right answer