Question 602757
assume that the rectangular piece of cardboard has length of L and width of W


L*W = 171
so L = 171/W


if the cardboard is cut 2 inch square each, the dimension of the box will be:
(L - 2*2)*(W - 2*2)*2 (length * width * height)


Volume of the box:
V = length * width * height
{{{150 = (171/W - 4)*(W - 4)*2}}}
{{{150/2 = (171/W - 4)*(W - 4)}}}
{{{75 = 171 - 684/W - 4W + 16}}}
(multiply all by W)
{{{75W = 171W - 684 -4W^2 + 16W}}}
{{{4W^2 + 75W - 171W - 16W + 684 = 0}}}
{{{4W^2 - 112W  + 684 = 0}}}
(divide all by 4)
{{{W^2 - 28W + 171 = 0}}}
{{{(W - 9)*(W - 19) = 0}}}
W - 9 = 0 or W - 19 = 0
W = 9 or W = 19
L = 171/9 = 19 or L = 171/19 = 9



so, the length and width of the cardboard used are 19 inch and 9 inch