Question

find rs.
t
34
r r u
rs

Explanation:

Step1: Identify Midsegments

Assume \( RQ = QU \) (from the marks) and \( S \) is midpoint of \( TU \), \( R \) is right angle. So \( RS \) is midsegment of \( \triangle TQU \).

Step2: Apply Midsegment Theorem

Midsegment length is half of the base. Wait, \( TR = 34 \)? Wait, maybe \( TR \) is 34, and \( RS \) is midsegment? Wait, no, maybe \( TR \) is 34, and \( RS \) is half? Wait, maybe the triangle is right - angled at \( R \), and \( S \) and \( Q \) are midpoints. So \( RS=\frac{1}{2}TU \)? No, wait, maybe \( TR = 34 \), and \( RS \) is half? Wait, maybe the length from \( T \) to \( R \) is 34, and \( RS \) is 17? Wait, no, let's re - examine. If \( S \) is the midpoint of \( TU \) and \( Q \) is the midpoint of \( RU \), then by midsegment theorem, \( RS\parallel QU \) and \( RS=\frac{1}{2}QU \)? No, maybe the vertical side \( TR = 34 \), and \( RS \) is half. Wait, maybe the problem is that \( R \) is a right angle, \( S \) is the midpoint of \( TU \), so in right - triangle \( TRU \), the midpoint of the hypotenuse \( TU \) is \( S \), and the midpoint of \( RU \) is \( Q \), then \( RS \) is midsegment, so \( RS=\frac{1}{2}TR \)? Wait, no, \( TR \) is 34, so \( RS = 17 \)? Wait, maybe the length of \( TR \) is 34, and \( RS \) is half of \( TR \) because \( S \) is the midpoint? Wait, maybe the diagram shows that \( TR = 34 \), and \( RS \) is half. So \( RS=\frac{34}{2}=17 \).

Answer:

\( 17 \)