Final answer:
To find the lengths of SV and QT, equate the length of TR to the sum of the lengths of SV and QT. Solve the resulting equation to find the value of x, and then substitute it back into the expressions for SV and QT.
Step-by-step explanation:
To find the lengths of SV and QT, we need to find the values of x. Based on the information given, the length of TR is 17 units. Looking at the given options, the correct answer is option d) (SV = 4x + 1) units, (QT = 9x - 4) units.
We can equate the length of TR to the sum of the lengths of SV and QT, since they all lie on the same line: 17 = SV + QT. Substituting the expressions for SV and QT, we get:
17 = (4x + 1) + (9x - 4).
Simplifying the equation gives:
17 = 13x - 3.
Adding 3 to both sides, we have:
20 = 13x.
Dividing both sides by 13, we find:
x = 20/13.
Substituting this value for x into the expressions for SV and QT gives the lengths:
SV = 4(20/13) + 1 = 80/13 + 1 = 93/13 units.
QT = 9(20/13) - 4 = 180/13 - 4 = 148/13 units.