Final answer:
To find the length of RO, we need to find the value of x and substitute it into the expression for RO. By applying the properties of a triangle and simplifying the equation, we can isolate RO and solve for its value.
Step-by-step explanation:
To find the length of RO, we need to find the value of x and substitute it into the expression for RO. To do this, we need to apply the properties of a triangle. We know that the sum of the lengths of the sides of a triangle is equal to the length of the third side. Therefore, we can write the equation: BR + RO = BO. Substituting the given expressions, we have (11x - 17) + RO = (9x + 6).
Simplifying the equation, we get 11x - 17 + RO = 9x + 6. Next, we can combine like terms by subtracting 9x from both sides: 11x - 9x - 17 + RO = 6. Simplifying further, we have 2x - 17 + RO = 6. Now, we can isolate RO by subtracting 2x and adding 17 to both sides: RO = 6 - 2x + 17. Finally, rearranging the terms, we get RO = 17 - 2x + 6, which can be simplified to RO = 23 - 2x.