Answer
$3.5cm\times13cm\times33cm$ or $5cm\times10cm\times30cm$
Work Step by Step
The three dimensions of the box can be expressed as $x, 40-2x, 20-2x$
and the known volume can be written as
$x(20-2x)(40-2x)=1500$
Plot this equation as shown, and we can find three x-intercepts $3.5,5,21.5$.
Discard the 21.5 as it does not give positive side lengths, we have $x=3.5 or 5cm$
The dimension of these two cases are $3.5cm\times13cm\times33cm$ or $5cm\times10cm\times30cm$
