OPRobert made a design on his wall with the similar pentagon tiles shownR9 cm9 cmKMQs15 cm10 cm10 cm15 cmUT10 cmP15 cmNnot drawn to scaleWhat is the length of side RS?3 cm

Since they are simmilar we will then have the following relationships.
[tex]\frac{15}{10}=\frac{9}{x}[/tex]Now, we solve for x, as follows:
[tex]x=\frac{9\cdot10}{15}\Rightarrow x=6[/tex]The expression goes along the lines of. 15 is to 10 what 9 is to x, with this as was done we solve for x and determine it's value, that since they keep proportionality.