ANSWER
The measure of side PR is
![10 \: cm](https://img.qammunity.org/2019/formulas/mathematics/middle-school/2h5or9jkesmntn21zo55iw8wj0l4cx9mqc.png)
Step-by-step explanation
Since the two triangles are similar, the ratio of corresponding sides are proportional.
This implies that,
![(|QR|)/(|KL|) = (|PR|)/(|JL|)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/1acpt4rhwz3wcs4kvmmw2c0wi7p2a0o96e.png)
We now substitute the values of the corresponding sides to obtain,
![(15)/(9) = (|PR|)/(6)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/oat9jcmvv4edruduoqv47g7uys35c0iagz.png)
We multiply both sides if the equation by 6 to obtain,
![(15)/(9) * 6= |PR|](https://img.qammunity.org/2019/formulas/mathematics/middle-school/zyzm0l5iygz8dgnbpzsfjm53nhq63mi7ff.png)
We simplify further to obtain,
![(15)/(3) * 2= |PR|](https://img.qammunity.org/2019/formulas/mathematics/middle-school/elpff0xi7vipvw62nfxyznbea8pk2gr35o.png)
![5 * 2= |PR|](https://img.qammunity.org/2019/formulas/mathematics/middle-school/7k90emdoc7t3hja51b37dl1a6revdfebf6.png)
![|PR| = 10 \: cm](https://img.qammunity.org/2019/formulas/mathematics/middle-school/oahn33czcpnvc0w3o2dggv28dq9bm2fbry.png)