Question

find the length of \\( \overline { s r } \\).

Explanation:

Step1: Check similarity

Since \( \frac{QF}{FS}=\frac{24}{12} = 2\), and \( \frac{33 - 11}{11}=2\), triangles \( QFE\) and \( QSR\) are similar by the Side - Side - Side (SSS) similarity criterion.

Step2: Use similarity ratio

Let \( SR=x\). The ratio of corresponding sides of similar triangles is equal. We know that the ratio of the sides of \(\triangle QFE\) to \(\triangle QSR\) is \( \frac{1}{2}\). Given \( FE = 8\), and using the ratio of sides of similar triangles \(\frac{FE}{SR}=\frac{QF}{QS}\). Since \( QS=33\), \( QF = 22\), \(\frac{8}{x}=\frac{22}{33}\). Cross - multiply: \(22x=8\times33\). Then \(x = 12\).

Answer:

\(36\)