Final answer:
To find the length of RT, set the expressions for RS, ST, and RT equal to each other and solve for x. Substitute x back into the expression for RT to find its length.
Step-by-step explanation:
To find the length of RT, we can set the expressions for RS, ST, and RT equal to each other and solve for x. The equation becomes (2x - 9) + (3x - 1) = 6x - 19. We can simplify this equation to 5x - 10 = 6x - 19. Subtracting 5x from both sides, we get -10 = x - 19. Adding 19 to both sides, we get 9 = x. Now, we can substitute x back into the expression for RT to find its length. RT = 6(9) - 19 = 54 - 19 = 35 units.