Final answer:
By setting the algebraic expressions for QS and TV equal to each other and solving for the variable V, it has been determined that the lengths of QS and TV are both 33 units.
Step-by-step explanation:
The question involves using algebra to solve for the lengths of two line segments where the lengths are described with expressions containing a variable V. Since the segments are part of triangles QRS and TUV, which are equal, the expressions for QS and TV can be set equal to each other and solved for V. Once the value of V is found, it can be substituted back into the expressions to find the actual lengths of QS and TV.
Starting with the equations given, QS = 4V + 5 and TV = 6V - 9, and setting them equal to each other because QRS = TUV, we get:
4V + 5 = 6V - 9
Solving for V, we have:
14 = 2V
V = 7
Using the value of V, we can find the lengths of QS and TV:
QS = 4(7) + 5 = 28 + 5 = 33
TV = 6(7) - 9 = 42 - 9 = 33
Therefore, the lengths of QS and TV are both 33 units.