Answer:
C. 19
Step-by-step explanation:
Since VZ = ZY, VW = WX therefore we can apply the midpoint theorem where a midpoint line is half of the base line.
Thus:
[tex]\displaystyle \large{ZW = \frac{1}{2}YX}\\\displaystyle \large{3x-5 = \frac{1}{2}(5x-2)}[/tex]
Then multiply both sides by 2 to get rid of the denominator and solve for x.
[tex]\displaystyle \large{(3x-5)2= \frac{1}{2}(5x-2)2}\\\displaystyle \large{6x-10= 5x-2}\\\displaystyle \large{6x-5x=-2+10}\\\displaystyle \large{x=8}[/tex]
Since we want to find the midpoint line or WZ, substitute x = 8 in 3x-5
[tex]\displaystyle \large{ZW = 3x-5}\\\displaystyle \large{ZW = 3(8)-5}\\\displaystyle \large{ZW = 24-5}\\\displaystyle \large{ZW =19}[/tex]
Therefore, ZW = 19
