Final answer:
To find the value of ST, we can use the Triangle Inequality Theorem and solve the inequality 6x + 2x > 8 to determine the value of x and then calculate ST.
Step-by-step explanation:
To find the value of ST, we need to use the given information that RS = 6x, ST = 2x, and RT = 8. Since RS and RT are the longer and shorter sides of the triangle respectively, we can apply the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, RS + ST must be greater than RT. Substituting the given values, we have 6x + 2x > 8. Simplifying the inequality, we get 8x > 8 and dividing both sides by 8 gives x > 1. Since x represents a positive number, we can conclude that ST = 2x = 2 * 1 = 2. Therefore, the answer is a. 2.