Chapter 8.7, Problem 20P

The given expression represents the area. Find the side length of the square.

$9y^2-24y+16$

To determine

To find the side length of the square whose area represented by the expression $9y^2-24y+16$

Answer to Problem 20P

The side length of the given square is $\left(3y-4\right)$ .

Explanation of Solution

Given information:

Given expression $9y^2-24y+16$

  

Given$9y^2-24y+16=\left({\left(3y\right)}^2-2\left(3y\right)4+4^2\right)$ is the expression that represents the area of the square.

As we know that $a^2-2ab+b^2={\left(a-b\right)}^2$

Put $a=3y,b=4$ , we get $\left({\left(3y\right)}^2-2\left(3y\right)4+4^2\right)={\left(3y-4\right)}^2$

Since area of the square is ${\left(side\right)}^2={\left(3y-4\right)}^2$

  $\Rightarrow side=\left(3y-4\right)$

Hence, the side length of the given square is $\left(3y-4\right)$ .