Final answer:
The correct answer is option d, where x equals 13, RZ is 30, and RT is 60. This is concluded by recognizing Z as the midpoint of RT and solving the equation 15x = 20 for x.
Step-by-step explanation:
The correct answer is option d. x = 13, RZ = 30, and RT = 60. When Z is the midpoint of RT, it implies that RZ is half the length of RT. Given that options a, b, and c provide RZ values that are not half of their corresponding RT values, they can be immediately discarded. Option d remains as it correctly suggests RZ is half of RT. The variable x corresponds to the value that solves the equation 15x = 20. When we solve this equation for x, we find that x indeed equals 13 (15 * 13 = 195, and 195/15 = 13). Therefore, Z, being the midpoint of RT, means that RZ is half of length RT, and since RT is 60, RZ must be 30.
To understand why, we need to know that the midpoint of a line segment is the point that divides the segment into two congruent parts. In this case, Z is the midpoint of RT, which means that RZ is equal to ZT.
Since RZ and ZT are congruent, we can set up the equation RZ = ZT. Substituting the given value for RZ (30), we have 30 = ZT. Since Z is the midpoint, ZT is also equal to RT, so we have 30 = RT. Therefore, x = 13, RZ = 30, and RT = 60.