Answer:
The answer is D
Step-by-step explanation:
In order to determine the "x" value, we use the thales theorem.
This theorem makes equalities between the sides and angles of a right triangle. I have attached an image that shows the equality we need.
Let me explain the image:
Let AD be perpendicular to BC. We have ∠ABC=∠DBA and ∠BAC=∠BDA=90°
So, hence by Thales theorem we have
:
[tex]\frac{AB}{BD}=\frac{BC}{BA}\\AB^2=BC*BD[/tex]
In this case, AB=x ; BD=7 and BC=13.
Then:
[tex]AB^2=BD*BC\\x^2=7*13\\x^2=91\\x=9.5[/tex]
Finally, the "x" value is 9.5
