Question

determining segment lengths
the length of tr is 17 units. what are the lengths of sv and qt?
sv =
units
qt =
units

Explanation:

Step1: Solve for \(x\)

Since \(QT = TS\) (properties of the figure), we have \(4x + 1=9x - 4\).

$$
LATEXBLOCK0
$$

Step2: Find \(SV\)

Substitute \(x = 1\) into \(SV=2(3x + 2)\) (because \(TR\) bisects \(SV\) and \(SR=RV\)).

$$SV=2(3\times1 + 2)=2\times5 = 10$$

Step3: Find \(QT\)

Substitute \(x = 1\) into \(QT=4x + 1\)

$$QT=4\times1+1=5$$

Answer:

\(SV = 10\) units, \(QT = 5\) units