Unless you want to use the formula for the solution of a cubic, trial and error is "the right way."

Let t be the "tall" dimension.

t(4t)(4t+5) = 2500

16t

4t

t=5 is a good first guess for a root. The other dimensions follow from that.

After finding the first root, the equation can be factored.

= (t-5)(4t

The quadratic has no real roots, so t=5 is the only real solution to our cubic.

Let t be the "tall" dimension.

t(4t)(4t+5) = 2500

16t

^{3}+20t^{2}-2500 = 04t

^{3}+ 5t^{2}- 625 = 0t=5 is a good first guess for a root. The other dimensions follow from that.

After finding the first root, the equation can be factored.

= (t-5)(4t

^{2}+ 25t + 125) = 0The quadratic has no real roots, so t=5 is the only real solution to our cubic.