Question 636313

{{{Volume = length*width*height}}}...where, in your case, {{{length=width}}}

so, {{{Volume = length^2*5cm}}}

{{{Surface_ area=SA) }}}...= >...surface areas of all the sides

Two sides have square areas and the other four sides have rectangular areas:

{{{SA = x^2 + x^2 + 5x + 5x + 5x + 5x }}}

{{{SA = 2x^2 + 20x }}}

given:  {{{SA=192}}}

{{{192=2x^2 +20x }}}

or
{{{2x^2 +20x=192}}}

{{{2x^2 +20x-192=0}}}......divide by {{{2}}} and solve for {{{x}}}

{{{x^2 +10x - 96 = 0}}}

{{{(x + 16)(x - 6) = 0}}}

{{{x = 6 cm}}} or {{{x=-16cm}}}

Pick only {{{x = 6 cm}}}, since length is {{{positive}}}.

Now use {{{x = 6cm}}} in the volume equation

{{{V = (6cm)^2*5cm = 36cm^2*5cm=180cm^3}}}