Question 1005809
h height
x each base dimension
volume is {{{hx^2}}}.
Given: {{{h=x+4}}}
volume is 225.


{{{(x+4)x^2=225}}}


{{{x^3+4x^2-225=0}}}


Several rational roots to try, such as  plus&minus of 1,3,5,15,25,9.  Be sure your first dividend for your synthetic divisions are  {{{x^3+4x^2+0*x-225}}}.  The rest of doing this process is now back to you to continue.


You will find a root of 5  corresponding to (x-5) factor, and the resulting {{{x^2+9x+45}}} as quadratic factor.  The quadratic factor here has only complex roots with imaginary component.


{{{highlight(x=5)}}} for a side of the square base.
------------and {{{highlight(h=9)}}}.