Since Ava constructed \( RA \) as a copy of \( TP \), the measure of \( RA \) will be the same as the measure of \( TP \). Given that \( TP = 189.34 \) millimeters, the measure of \( RA \) is also:
\[ \text{The measure of } RA = 189.34 , \text{millimeters}. \]