Chapter 8, Problem 67SGR

To determine

To calculate the width of the rectangle.

Answer to Problem 67SGR

  $(3x-7)$

Explanation of Solution

Given:

  

Length of the rectangle $=2x-1$

Area of the rectangle $=6x^2+11x-7$

Formula used:

Area of the rectangle $=l\times b$

Calculation:

Given that the area of the rectangle is $6x^2+11x-7$ and the length of the rectangle is $2x-1$.

Substituting the given values in the formula,

Area of the rectangle $=l\times b$

  $\begin{array}{c}\Rightarrow 6x^2+11x-7=(2x-1)\times b\\ \Rightarrow 6x^2+11x-7=(2x-1)b\\ \Rightarrow \frac{6x^2+11x-7}{2x-1}=b\end{array}$

  $(2x-1)\begin{array}{c}\hfill 3x-7\\ \hfill \overline{)\begin{array}{l}6x^2+11x-7\\ \frac{6x^2-3x}{\begin{array}{l}14x-7\\ \frac{-14x+7}{0}\end{array}}\end{array}}\end{array}$

  $\begin{array}{l}\Rightarrow \frac{6x^2+11x-7}{2x-1}=b\\ \Rightarrow 3x-7=b\\ \Rightarrow b=3x-7\end{array}$

Conclusion:

Therefore, the width of the rectangle is $(3x-7).$