After plotting the data where x=area, and f(x)=the length of one side of the square, Sam determined the model to approximate the side of a square was Use the model Sam created to predict the side length of the square when the area is 86. 6

Answer:The side length is 9.306 approximately .Step-by-step explanation:Consider the provided information:x axis represents the area and y axis represents the side of the square.The are of square can be calculated as:[tex]area=(side)^{2}[/tex] or [tex]x=(y)^{2}[/tex]Hence model would be:[tex]side=\sqrt{area}[/tex] or [tex]y=\sqrt{x}[/tex]Since, the area is:x = 86.6Substitute value of x in [tex]y=\sqrt{x}[/tex].[tex]y=\sqrt{86.6}[/tex][tex]y=9.306[/tex]The length of the side is 9.306 approximately .Check:Calculate the area if side = 9.306[tex]x=(9.306)^{2}[/tex][tex]x=86.60[/tex]Hence, the side length is 9.306 approximately .