Question

part 2: free response questions: directions: show all of your work. an answer with no work will receive one point. you may earn partial credit for each question.

1. (4 points) in the diagram below, \\( \overline { u t } \parallel \overline { r q } \\) and \\( \delta t s u \sim \delta q s r \\). if \\( s u = 7.5 \\), \\( q s = 16 \\), and \\( t s = 12 \\), find the length of \\( \overline { s r } \\). figures are not necessarily drawn to scale.

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle TSU\sim\triangle QSR\), the ratios of corresponding sides are equal. That is \(\frac{TS}{QS}=\frac{SU}{SR}\).

Step2: Substitute the given values into the proportion

We know that \(TS = 12\), \(QS=16\), and \(SU = 7.5\). Substituting these values into \(\frac{TS}{QS}=\frac{SU}{SR}\), we get \(\frac{12}{16}=\frac{7.5}{SR}\).

Step3: Solve for \(SR\)

Cross - multiply: \(12\times SR=16\times7.5\). Then \(12SR = 120\). Divide both sides by 12: \(SR=\frac{120}{12}=10\).

Answer:

\(10\)