Chapter 8.7, Problem 7STP

A four-sided building has an area of $36x^2+48x+16.$

Explain how to find a possible length and width of the building. What is a possible shape of the building?

To determine

To find the possible length and width of the building, whose four sided building has an area represented by the expression $36x^2+48x+16$ and hence what is the possible shape of the building ?

Answer to Problem 7STP

The side length of the given square shaped building is $\left(6x+4\right)$ .

Explanation of Solution

Given information:

Given expression $36x^2+48x+16$ is the expression that represents the area of the four sided building.

Given$36x^2+48x+16=\left({\left(6x\right)}^2+2\left(6x\right)4+{\left(4\right)}^2\right)$ 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 $a=6x,b=4$ , we get $\left({\left(6x\right)}^2+2\left(6x\right)4+{\left(4\right)}^2\right)={\left(6x+4\right)}^2$

Thus, ${\left(6x+4\right)}^2$ is equivalent to area of the square as ${\left(6x+4\right)}^2={\left(side\right)}^2$

  $\Rightarrow side=\left(6x+4\right)$

Hence, the side length of the given square shaped building is $\left(6x+4\right)$ .