Answer:
Option C is the correct choice.
Step-by-step explanation:
We have been given that Z is the midpoint of line segment RT. We are asked to find the value of x, RZ and RT.
Since Z is the midpoint of line segment RT, so RZ will be equal to ZT. So, we can set an equation as:
[tex]RZ=ZT[/tex]
[tex]8x-10=150[/tex]
[tex]8x-10+10=150+10[/tex]
[tex]8x=160[/tex]
[tex]\frac{8x}{8}=\frac{160}{8}[/tex]
[tex]x=20[/tex]
Therefore, the value of x is 20.
To find the value of RZ, we will substitute [tex]x=20[/tex] in expression [tex]8x-10[/tex] as:
[tex]RZ=8(20)-10[/tex]
[tex]RZ=160-10[/tex]
[tex]RZ=150[/tex]
Therefore, the length of RZ is 150 units.
Since Z is the midpoint of line segment RT, so length of RT would be 2 times length of RZ.
[tex]RT=2*RZ[/tex]
[tex]RT=2*150[/tex]
[tex]RT=300[/tex]
Therefore, the length of RT is 300 units.
