Respuesta :
Answer: VT = 8
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Work Shown:
V is the midpoint of RT, so RV = VT
RV = 2x+4
VT = RV = 2x+4
RV+VT = RT ... by the segment addition postulate
RV+RV = RT ... replace VT with RV
2*(RV) = RT
2*(2x+4) = 8x .... plug in the given expressions
4x+8 = 8x
8 = 8x-4x
8 = 4x
4x = 8
x = 8/4
x = 2
Which means,
RV = 2x+4 = 2*2+4 = 8
VT = RV = 8
RT = 8x = 8*2 = 16
Note how
RV+VT = 8+8 = 16
which matches with the length of RT to help confirm our answer.
Answer:
[tex] \boxed{line \: vt \: = 8.}[/tex]
Step-by-step explanation:
[tex]if \: \boxed{ line\: rt} = \boxed{ line\: rv} + \boxed{ line\: vt} = 8x \\ then \: \boxed{ line\: rv} = \boxed{ line\: rt} = 2x + 4 \\ hence \to \\ 2(2x + 4) = 8x \\ 4x + 8 = 8x \\ 4x = 8 \\ \boxed{x = 2} \\ \\ if \: x = 2 :then \: \\ 2x + 4 = 2(2) + 4 = 8. \\ therefore \: \boxed{ line\: vt = 8.} [/tex]
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