Question

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Answer 1

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:

$\displaystyle \large{ZW = \frac{1}{2}YX}\\\displaystyle \large{3x-5 = \frac{1}{2}(5x-2)}$

Then multiply both sides by 2 to get rid of the denominator and solve for x.

$\displaystyle \large{(3x-5)2= \frac{1}{2}(5x-2)2}\\\displaystyle \large{6x-10= 5x-2}\\\displaystyle \large{6x-5x=-2+10}\\\displaystyle \large{x=8}$

Since we want to find the midpoint line or WZ, substitute x = 8 in 3x-5

$\displaystyle \large{ZW = 3x-5}\\\displaystyle \large{ZW = 3(8)-5}\\\displaystyle \large{ZW = 24-5}\\\displaystyle \large{ZW =19}$

Therefore, ZW = 19