Chapter 11.3, Problem 16PPS

To determine

To Find: The area of the base of the prism.

Answer to Problem 16PPS

  $area=\frac{3x^3+34x^2+72x-64}{x+4}$

Explanation of Solution

Given:The volume of the rectangular prism is $3x^3+34x^2+72x-64$ and the height is $x+4$

Given: $3x^3+34x^2+72x-64$

  $\begin{array}{l}volume=length\times width\times height\\ area=length\times width\\ i.e.\\ volume=area\times height\end{array}$

Volume = $3x^3+34x^2+72x-64$

Height= $x+4$

Now

  $\begin{array}{l}volume=area\times height\\ 3x^3+34x^2+72x-64=area(x+4)\\ area=\frac{3x^3+34x^2+72x-64}{x+4}\end{array}$

Hence,

  $area=\frac{3x^3+34x^2+72x-64}{x+4}$