Since RO, OS, SA, AL are congruent with each other and RL = 52, the length of segment RO is 13 units.
Based on the definition of a line segment and the segment addition postulate, we have the following congruent segments;
RO = OS = SA = AL
RO + OS + SA + AL = RL
By substituting the given length of segment OS, we have the following;
6x - 34 + 6x - 34 + 6x - 34 + 6x - 34 = 52
24x - 136 = 52
24x = 52 + 136
24x = 188
x = 188/24
x = 47/6
Now, we can determine the length of segment RO as follows;
RO = 6x - 34
RO = 6(47/6) - 34
RO = 47 - 34
RO = 13 units.
Complete Question:
Knowing that RO, OS, SA, AL are congruent with each other and RL= 52, find RO.