Chapter 8.2, Problem 35E

To determine

the dimensions of the original patio.

Answer to Problem 35E

The dimension of the original patio is: 12 ft. by 12 ft.

Explanation of Solution

Given information:

The area of the original square patio of side length x feet: $A=x^2$

When 48 square feet is added to this area, it results in a total area of 192 square feet.

From the given data it can be said that,

  $\begin{array}{c}A+48=192\\ x^2+48=192\\ x^2=192-48\end{array}$

  $\begin{array}{c}{x}^2=144\\ x=\pm 12\end{array}$

But x represents the side length of the patio, so it can’t be negative.

So, the side length of the original patio is $x=12$ .

This can also be observed from the graph of $A=x^2+48$ that when 48 square feet is added to the original area, it results in a total area of 192 square feet (that is when $x=12$ , $A=192$ ).

  

Conclusion:

The dimension of the original patio is: 12 ft. by 12 ft.