Chapter 8, Problem 20PT

To determine

To calculate the length of the room.

Answer to Problem 20PT

  $x-10$

Explanation of Solution

Given:

  $\text{Area of rectangle}$

  $=x^2-100$

  $\text{Width of room}=x-10$

Formula used:

  $\text{Area of rectangle}$

  $=l\times w$

Calculation:

Substituting the area and width in the area of the rectangle,

  $\text{Area of rectangle}$

  $=l\times w$

  $\begin{array}{l}\Rightarrow x^2-100=l\times (x-10)\\ \Rightarrow \frac{x^2-100}{x-10}=l\end{array}$

Hence,

  $x-10\begin{array}{c}\hfill x-10\\ \hfill \overline{)\begin{array}{l}{x}^2-100\\ \frac{x^2-100}{0}\end{array}}\end{array}$

  $\begin{array}{l}\Rightarrow \frac{x^2-100}{x-10}=l\\ \Rightarrow x-10=l\\ \Rightarrow l=x-10\end{array}$

Conclusion:

Therefore, the length of the room is $x-10.$