Question

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Answer 1

C. 19

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 = (1)/(2)YX}\\\displaystyle \large{3x-5 = (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= (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