Final answer:
The problem involves finding the length of a bisected line segment PQ. After solving the equation that equates the two halves, PR and RQ, we find the total length of PQ to be 10 units.
Step-by-step explanation:
The question concerns the concept of a line segment being bisected at a point, meaning the segment is divided into two equal parts at that point. In this case, PQ is bisected at R, which means PR and RQ are equal in length.
Since PR is given as 2x + 21 and RQ is given as x + 13, we can write an equation to find the value of x based on the fact that PR = RQ:
2x + 21 = x + 13
Solving for x gives us:
x = 13 - 21
x = -8
Since x is negative and lengths cannot be negative, there must be an error or misinterpretation in the definition of the lengths given for PR and RQ.
However, assuming the values are correct and the question is about finding the total length of PQ, we can express PQ as PR + RQ.
Substituting the expressions for PR and RQ gives us (2x + 21) + (x + 13), which simplifies to 3x + 34.
Using the found value of x, PQ = 3(-8) + 34
= -24 + 34
= 10.
Therefore, the length of PQ is 10 units.