Question 726739
Such an evil problem! It's trying to trick us two ways.
The shoebox-like prism has a length, L, a width, W, and a height, H, that are all fractional quantities of inches.
However, those numbers do not matter, given the question at the end.
When you enlarge dimensions by a factor of {{{x}}},
the surface area of a solid changes by a factor of {{{x^2}}} and the volume by a factor of {{{x^3}}}.
That happens because you have to multiply pairs of dimensions to get surface area, so when you multiply each pair, you get an {{{x^2}}} as a factor.
A face that had an area of {{{LW}}} gets it changed to {{{(Lx)(Wx)=LWx^2}}} .
A face that had an area of {{{LH}}} gets it changed to {{{(Lx)(Hx)=LHx^2}}} .
A face that had an area of {{{HW}}} gets it changed to {{{(Hx)(Wx)=HWx^2}}} .
 
The scale factor was {{{1&1/2=3/2}}}
The dimensions of the large prism are {{{3/2}}} of the dimensions of the small one.
The dimensions of the small prism are {{{2/3}}}={{{1/((3/2))}}} of the dimensions of the large one.
{{{(2/3)^2=4/9}}}
The surface area of the original (smaller) prism is {{{highlight(4/9)}}} times as much as the surface area of the larger right rectangular prism.