Question 253379
let x = side of square to be cut.


volume of box will be:


(11-2x)*(8.5-2x)*x = 48


multiply out the factors to get:


4x^3 - 39x^2 + 93.5x = 48


substitute the values for x in each of the possible solutions to get:


selection a = 3.65 yielding y = 16.206
selection b = 2.66 yielding y = 48.045984
selection c = .71 yielding y = 48.156744
selection d = .57 yielding y = 41.364672


graph the equation y = 4x^3 - 39x^2 + 93.5x against the line y = 48 to see how this relates to the solutions.


{{{graph (600,600,-10,10,-200,200,4x^3 - 39*x^2 + 93.5x,48)}}}


you can see that there are 3 points where the graph of the equation intersect with y = 48.


those points are around .71, 2.66, and 6.something.


6.something was not one of the possible solutions.


.71 and 2.66 were.


the results show that both of these points are closer than the others with 2.66 being the closest.