See attachment...


Question 9 of 10
What is the value of m in the figure below? In this diagram, AABD ~ ABCD.
14
D
5
B
M
C
A. √70
B. 221
√95
D. √48
E. √323
F. √650

See attachment Question 9 of 10 What is the value of m in the figure below In this diagram AABD ABCD 14 D 5 B M C A 70 B 221 95 D 48 E 323 F 650 class=


Answer :

Answer:

  C.  √95

Step-by-step explanation:

You want the length of the segment marked m in the right triangle figure shown.

Similar triangles

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]

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Additional comment

For the purpose here, we don't care about ∆ABD. We are only concerned with ∆ABC and ∆BDC.