Chapter 11.5, Problem 4CYP

To determine

To calculate: To find the length of rectangle

Answer to Problem 4CYP

The length of rectangle is $2x+8+\frac{9}{x+1}$

Explanation of Solution

Given information: The area of a rectangle is $\left(2x^2+10x-1\right)$ square units, and the width is $\left(x+1\right)$ units

Formula Used:

Long division is the division of whole number in a systematic procedure to derive the answer.

Area of rectangle is calculated as

  $Area=Length\times Width$

Calculation:

Given that the area of a rectangle is $\left(2x^2+10x-1\right)$ square units, and the width is $\left(x+1\right)$ units.

Length of rectangle is calculated as

  $Area=Length\times Width$

  $Length=\frac{Area}{Width}$

Substituting the values,

  $Length=\frac{\left(2x^2+10x-1\right)}{x+1}$

Dividing the polynomial with the divisor to derive the quotient and remainder

  $x+1\begin{array}{c}\hfill 2x+8\\ \hfill \overline{)\begin{array}{l}2x^2+10x-1\\ 2x^2+2x\\ --\\ -------\\ 0+8x-1\\ +8x+8\\ --\\ -------\\ \text{ 9}\end{array}}\end{array}$

Thus, quotient is $2x+8+\frac{9}{x+1}$

Conclusion:

Hence, the length of rectangle is $2x+8+\frac{9}{x+1}$