Answer
$16x+12$
Work Step by Step
$V = base * height * length$
Since the length and the height are part of a square, we can say $height = length$. Thus,
$V = base * height^2$
$V = 144x^3 + 216x^2+81x$
$144x^3+216x^2+81x$
$3x(48x^2+72x+27)$
$3x*3(16x^2+24x+9)$
$9x(16x^2+24x+9)$
$9x(16x^2+12x+12x+9)$
$9x[4x(4x+3)+3(4x+3)]$
$9x[(4x+3)(4x+3)]$
$9x(4x+3)(4x+3)$
$9x$, $(4x+3)$, and $(4x+3)$ are the dimensions of the prism. Since $(4x+3)$ is listed twice, we know this is the height and the length.
perimeter = side + side + side + side
$perimeter = 4*side$
$P = 4*(4x+3)$
$P = 16x+12$
