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, it follows that:
\[ RA = 189.34 \text{ millimeters} \]
So, the measure of \( RA \) is 189.34 millimeters.