Answer:
C. √95
Step-by-step explanation:
You want the length of the segment marked m in the right triangle figure shown.
All of the right triangles in this figure are similar by the AA postulate. That means the ratios of short side to hypotenuse are the same for the largest and smallest triangles:
[tex]\dfrac{\text{short side}}{\text{hypotenuse}}=\dfrac{m}{5+14}=\dfrac{5}{m}\\\\m^2=5\cdot19\\\\\boxed{m=\sqrt{95}}\qquad\text{matches choice C}[/tex]
__
Additional comment
For the purpose here, we don't care about ∆ABD. We are only concerned with ∆ABC and ∆BDC.