well a cube has 6 squared area on its surface

and each of it can be given as x^2. hence in a total there will be 6(x^2) total area surface of a cube.(where x = length of one side of the cube)

given in your question that the total area of that particular cube is 1350

hence from total surface area = 6(area of one square surface of a cube)

1350 = 6(x^2)

x^2 = 225

x = 15 inches

Surface Area Formulas

this will give you a better idea on it