Final answer:
D) 13. To deduce the length of RS in the given collinear line segment, we add the expressions for RS and ST and set them equal to the given total length of RT. Solving for W and substituting back into the expression for RS yields the length of RS as 13 units.
Step-by-step explanation:
To find the length of RS in a collinear line segment when RS is represented as 2W + 1, ST is represented as W - 1, and RT is given as 18, we must first understand that since RS, ST, and RT are collinear and consecutive, the length of RT is the sum of the lengths of RS and ST. Therefore, we can set up the following equation:
RT = RS + ST
18 = (2W + 1) + (W - 1)
Simplifying the equation:
18 = 3W
Dividing both sides by 3 to solve for W:
W = 6
Now that we have found W, we can determine the length of RS:
RS = 2W + 1 = 2(6) + 1 = 12 + 1 = 13
The length of RS is therefore 13 units.