Respuesta :
The Ratio OP: PQ: QR = 5: 6: 1 means that if the line segment OR is 5 + 6 + 1 = 12 then
[tex]\frac{OP}{OR}=\frac{5}{12}[/tex][tex]\frac{PQ}{OR}=\frac{6}{12}[/tex][tex]\frac{QR}{OR}=\frac{1}{12}[/tex]But, the problem is that OR is not 12, rather, it is 36; therefore, we need to multiply the ratios above by 36:
[tex]\begin{gathered} \frac{OP}{OR}=\frac{5}{12}\rightarrow OP=\frac{5}{12}OR \\ \end{gathered}[/tex][tex]OP=\frac{5}{12}\times36[/tex][tex]OP=15[/tex][tex]\frac{PQ}{OR}=\frac{6}{12}\rightarrow PQ=\frac{6}{12}\times OR[/tex][tex]PQ=\frac{6}{12}\times36[/tex][tex]PQ=18[/tex][tex]\frac{QR}{OR}=\frac{1}{12}\rightarrow QR=\frac{1}{12}\times OR[/tex][tex]QR=\frac{1}{12}\times36[/tex][tex]QR=3[/tex]Hence, we have the lengths OP, PQ, and QR.
The line segment OQ is
[tex]OQ=OP+PQ[/tex]therefore,
[tex]OQ=15+18[/tex][tex]OQ=33.[/tex]which is our answer!
