Question 130510
the side of the square will be the depth of the tank
__ the length and width of the tank will be the the length, 10ft, and width, 8ft, of the sheet
__ each dimension reduced by twice the side of the square - a square is cut from each end


the volume is length times width times depth __ let x="side of square"
__ so volume=(10-2x)(8-2x)(x) __ 48=80x-36x^2+4x^3


4x^3-36x^2+80x-48=0 __ dividing by 4 __ x^3-9x^2+20x-12=0


possible values for x are the factors of -12 __ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12
__ 1 satisfies the equation, so x-1 can be factored out


factoring __ (x-1)(x^2-8x+12)=0 __ factoring again __ (x-1)(x-2)(x-6)=0


1, 2, and 6 all satisfy the equation
__ but in real life, you can't cut a 6ft square from all 4 corners of an 8ft by 10ft sheet