# How do you find the the length, width and height of rectangular prism if the volume is h^3+h^2-20h cubic meters?

If l=length , w=width, h=height of the prism the volume is

$V = l \cdot w \cdot h$

But we know that $V = {h}^{3} + {h}^{2} - 20 h$ hence

$l \cdot w \cdot h = {h}^{3} + {h}^{2} - 20 h$

$\frac{l \cdot w \cdot h}{h} = \frac{{h}^{3} + {h}^{2} - 20 h}{h}$

$l \cdot w = {h}^{2} + h - 20$

$l \cdot w = \left(h + 5\right) \cdot \left(h - 4\right)$

From the last equation we find that $l = \left(h + 5\right)$ m and $w = \left(h - 4\right)$ m and $h = h$ m