Question 25
A rectangular box has sides $x \lt y \lt z$. Its perimeter is $p = 4(x + y + z)$, its surface area is $s = 2(xy + yz + zx)$ and its main diagonal has length $d = \sqrt{x^2 + y^2 + z^2}$. Show that $3x \lt (p/4 - \sqrt{d^2 - s/2})$ and $3z \gt (p/4 + \sqrt{d^2 - s/2})$.