Chapter 8, Problem 10PT

To determine

To calculate the width of the rectangle

Answer to Problem 10PT

  $x-3$

Explanation of Solution

Given:

  $\text{Area of rectangle}=2x^2-x-15$

Formula used:

  $\text{Area of rectangle}$

  $=l\times w$

Calculation:

From the given figure,

  $\text{Length of rectangle}$

  $=2x+5$

Substituting the area and length in the area of the rectangle formula,

  $\text{Area of rectangle}$

  $=l\times w$

  $\begin{array}{l}\Rightarrow 2x^2-x-15=(2x+5)\times w\\ \Rightarrow \frac{2x^2-x-15}{2x+5}=w\end{array}$

Hence,

  $2x+5\begin{array}{c}\hfill x-3\\ \hfill \overline{)\begin{array}{l}2x^2-x-15\\ \frac{\frac{2x^2+5x}{\begin{array}{l}-6x-15\\ -6x-15\end{array}}}{0}\end{array}}\end{array}$

  $\begin{array}{l}\Rightarrow \frac{2x^2-x-15}{2x+5}=w\\ \Rightarrow x-3=w\\ \Rightarrow w=x-3\end{array}$

Conclusion:

Therefore, the width of the rectangle is $x-3.$