Chapter 11.4, Problem 6MCQ

To determine

The length of the prism

Answer to Problem 6MCQ

The length of the prism is $w+2$ .

Explanation of Solution

Given:

The height of a rectangular prism is 3 more than twice its width w and the volume of the prism is $2w^3+7w^2+6w$

  $\begin{array}{l}Width=w\\ Height=2w+3\end{array}$

Concept Used:

Volume of prism is $V=bh$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the length of the prism as shown below,

  $\begin{array}{c}V=2w^3+7w^2+6w\\ V=w\left(2w^2+7w+6\right)\\ V=w\left(2w^2+4w+3w+6\right)\\ V=w\left(2w\left(w+2\right)+3\left(w+2\right)\right)\\ V=w\left(2w+3\right)\left(w+2\right)\end{array}$

Thus, the length of the prism is $w+2$ .