x = depth
4x = width
4х+5 = height
[tex]x*4x*(4x+5)=2500 \\ 4x^2(4x+5)=2500\\
16x^3+20x^2-2500 = 0 \ \ |:4 \\ 4x^3 +5x^2-625=0 \\ 4x^3-20x^2+25x^2-625=0 \\ 4x^2(x-5)+25(x^2-25)=0 \\ 4x^2(x-5)+25(x-5)(x+5)=0 \\ (x-5)(4x^2+25(x+5))=0 \\ (x-5)(4x^2+25x+125)=0\\x-5=0 \ \ \ \ \ or \ \ \ 4x^2+25x+125=0 \\ \boxed{x=5} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ D=25^2-4*4*125=-1375 \to \ no \ real \ solutions [/tex]
We got one solution x=5. Let's find the measurements of the container:
depth = x = 5 cm
width = 4x = 4*5 = 20 cm
height = 4x+5 = 4*5+5 = 25 cm
