Question

in the diagram, tq is 18 units in length. what is the length of rs? 16 units 18 units 25 units 46 units

Explanation:

Step1: Identify congruent segments

Since line \(l\) is the perpendicular - bisector of \(\overline{RQ}\), we know that \(\overline{RT}=\overline{TQ}\) and \(\overline{RS}=\overline{SQ}\). Given \(TQ = 18\) units, then \(RT=18\) units. Also, since \(\overline{RS}=\overline{SQ}\), we have \(2x + 10=9x-11\).

Step2: Solve the equation for \(x\)

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Step3: Find the length of \(\overline{RS}\)

Substitute \(x = 3\) into the expression for \(RS\) (either \(2x + 10\) or \(9x-11\)). Using \(2x + 10\), we get \(2\times3+10=6 + 10=16\) units. Using \(9x-11\), we get \(9\times3-11=27-11 = 16\) units.

Answer:

16 units