Acertain rectangular box has a volume of 144 cubic inches, a surface area of 192 square inches, and a height one inch greater than its width. what is the distance from one corner of the box to the diagonally opposite corner?

h = w + 1
so (w + 1)(lw) = 144 so l = 144 / (w^2 + w)
and 2(lw + w(w + 1) + l(w + 1)) = 192 or (lw + w(w + 1) + l(w + 1)) = 96
now (144 / (w^2 + w) * w + w(w + 1) + 144 / (w^2 + w) * (w + 1)) = 96
or (144 / (w + 1) + w(w + 1) + 144 / (w) - 96 = 0
Now graph this on your calculator to find w
w = 3 or 7.1421
Thus H = 4 or 8.1421
Thus because w * l * h = 144, l = 12, 2.4763
Thus we are trying to solve for sqrt(l^2 + h^2 + w^2) so plugging in we get:
13 or 11.11

I would just use the first numbers(w = 3, h = 4, l = 12, diagonal = 13)