A certain 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)