Question 296244
If L and W are the length and width, respectively, of the original piece of cardboard, and the cut-out corners are 2X2 inches, then the volume (V) of the newly-formed open top box with a height (h) of 2 inches can be expressed as:
{{{V = (L-4)*(W-4)*h}}} Substitute {{{L = W+6)}}}
{{{V = ((W+6)-4)*(W-4)*2}}} and the volume of this box is given as {{{V = 110}}}cu.in., so we can write:
{{{110 = (W+2)*(W-4)*2}}} Simplify and solve for W.
{{{110 = 2(W^2-2W-8)}}} Divide both sides by 2.
{{{55 = W^2-2W-8}}} Subtract 55 from both sides.
{{{W^2-2W-63 = 0}}} Solve by factoring.
{{{(W+7)(W-9) = 0}}} so that...
{{{W = -7}}} or {{{W = 9}}} Discard the negative solution as the width W is a positive quantity.
{{{highlight(W = 9)}}}inches. and...
{{{L = W+6}}}
{{{highlight(L = 15)}}}inches.