Chapter 8.7, Problem 22PPE

To determine

To find the side length of the given square

  

Answer to Problem 22PPE

The side length of given square is $\left(8r-9\right)$ .

Explanation of Solution

Given information:

Given square

  

As we have area of the square in terms of a polynomial in variable $r$ is $64r^2-144r+81$

  $\begin{array}{l}\Rightarrow 64r^2-144r+81={\left(8r\right)}^2-2\left(8r\right)\left(9\right)+{\left(9\right)}^2\\ From{a}^2+2ab+b^2={\left(a+b\right)}^2\\ \Rightarrow {\left(8r\right)}^2-2\left(8r\right)\left(9\right)+{\left(9\right)}^2={\left(8r-9\right)}^2\\ \therefore 64r^2-144r+81={\left(8r-9\right)}^2\end{array}$

  $\begin{array}{l}\text{Thus,}Area={\left(side\right)}^2={\left(8r-9\right)}^2\\ \Rightarrow \text{side}=\left(8r-9\right)\end{array}$

Hence, the side length of given square is $\left(8r-9\right)$ .