Answer
$5,5,8$.
Work Step by Step
Let $x$ be the length of the side of the base. Then our equation for the volume is: $x\cdot x(x+3)=200\\x^3+3x^2-200=0\\(x-5)(x^2+8x+40)=0$
The quadratic polynomial has a positive discriminant; thus it cannot be $0$, and $x-5=0\\x=5$.
Thus the dimensions are: $5,5,8$.
