Question 863163
x for length
y for width
x=y+3
The square of side size 1.5 inches being removed before folding the flaps means that height will be 1.5 inches.


Cutting the specified corner piece makes these variable dimensions for the base:
(x-2(1.5)) and (y-2*1.5), meaning x-3 and y-3.  Using substitution for x as described means that the dimensions are:
{{{x-3=(y+3)-3=highlight_green(y)}}} for the LENGTH of the base!
and
{{{highlight_green(y-3)}}} for the WIDTH of the base.


Formulate the volume equation.
{{{y(y-3)(1.5)=162}}}
-
Simplify the volume equation.
{{{y^2-3y=162/1.5}}}
{{{y^2-3y-108=0}}}
Which is factorable:
{{{(y+9)(y-12)=0}}}
The sensible answer is {{{highlight(y=12)}}} for the WIDTH.
Finding x, x=y+3, {{{x=12+3=15}}}, {{{highlight(x=15)}}} for the LENGTH.