Question

in the diagram, the length of segment tq is 40 units. what is the length of segment qv? 32 units 36 units 40 units 44 units

Explanation:

Step1: Set up equation for \(x\)

Since \(SR\) is the perpendicular bisector of \(TV\), \(ST = SV\). So \(2x + 8=3x - 4\).
Solve for \(x\):

$$
LATEXBLOCK0
$$

Step2: Find \(TV\)

First, find \(ST\) by substituting \(x = 12\) into \(2x + 8\): \(2\times12+8=32\).
Since \(SR\) is the perpendicular bisector of \(TV\), \(TR = RV\) and \(\angle SRT=\angle SRV = 90^{\circ}\), \(SR = SR\) (common side). So \(\triangle STR\cong\triangle SRV\) (by SAS congruence). Then \(TQ = QV\) (corresponding parts of congruent triangles).

Answer:

\(40\) units