Chapter 11.5, Problem 40PPS

To determine

To calculate: To find the expression for missing length of rectangle

Answer to Problem 40PPS

The missing length of rectangle is $2x+4$

Explanation of Solution

Given information: Area of rectangle is $A=4x^2+16x+16$ and width is $2x+4$

Formula Used:

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

Calculation:

Given the area of rectangle is $A=4x^2+16x+16$ and width is $2x+4$

Length of rectangle is calculated as follows:

  $\begin{array}{l}Length=\frac{Area}{Width}\\ Length=\frac{4x^2+16x+16}{2x+4}\end{array}$

Dividing the polynomial with the divisor to derive the missing length

  $2x+4\begin{array}{c}\hfill 2x+4\\ \hfill \overline{)\begin{array}{l}4x^2+16x+16\\ 4x^2+8x\\ --\\ --------\\ 0+8x+16\\ +8x+16\\ --\\ --------\\ \text{ 0}\end{array}}\end{array}$

Thus, the length is $2x+4$

Conclusion:

Hence, the missing length of rectangle is $2x+4$