PR=45
Explanation
Step 1
as the triangles are similar, the ratio of the smaller side to the longest side must be equal,so
[tex]\text{ratio}=\frac{smaller\text{ length}}{\text{longest length}}=\frac{green\text{ length}}{\text{black length}}[/tex]so
[tex]\begin{gathered} \text{ratio}1=\text{ratio}2 \\ \frac{18}{20}=\frac{PR}{50} \end{gathered}[/tex]Step 2
solve for PR
[tex]\frac{18}{20}=\frac{PR}{50}[/tex]cross multiply
[tex]\begin{gathered} \frac{18}{20}=\frac{PR}{50} \\ 18\cdot50=20\cdot PR \\ 900=20PR \end{gathered}[/tex]divide both sides by 20
[tex]\begin{gathered} 900=20PR \\ \frac{900}{20}=\frac{20PR}{20} \\ 45=PR \end{gathered}[/tex]so, the answer is 45
I hope this helps you
