Hello!
We can first find RZ. A midpoint is the point right in the middle of a line segment. It splits the line into two equivalent lengths. If z is the midpoint of RT, it therefore splits RT into two equivalent segments, RZ and ZT. Thus, the length of RZ is equivalent to ZT, therefore, the length of RZ is 150.
Next, find RT. We know that RT is made of RZ and ZT, and we know the side lengths of both - 150 and 150. Therefore, add these two together to get the length of RT. 150 + 150 = 300.
Finally, find x. We know that RZ is equal to 150, and we are given 8x - 10 = RZ. Therefore, we know 8x - 10 = 150. Solve this equation for x by isolating x.
8x - 10 = 150
8x = 160
x = 20
Therefore, x = 20.
Your final answer is choice C: x = 20, RZ = 150, and RT = 300.
Hope this helps!
