Chapter 7.4, Problem 87PFA

To determine

To calculate the area of the square in simplified form

Answer to Problem 87PFA

288

Explanation of Solution

Formula used:

Area of square = $a^2$ where a is the side of the square.

Calculation:

Given that the side of the square is $5\sqrt{18}-3\sqrt{2}$

Simplify the expression,

  $\begin{array}{l}\Rightarrow 5\sqrt{18}-3\sqrt{2}\\ \Rightarrow 5\sqrt{9\times 2}-3\sqrt{2}\\ \Rightarrow 5\times 3\sqrt{2}-3\sqrt{2}\\ \Rightarrow 15\sqrt{2}-3\sqrt{2}\\ \Rightarrow 12\sqrt{2}\end{array}$

Therefore, the side of the square is $12\sqrt{2}$ .

Substitute in the formula of area,

  $\begin{array}{c}A=a^2\\ ={\left(12\sqrt{2}\right)}^2\\ =12\sqrt{2}\times 12\sqrt{2}\\ =144\times 2\\ =288\end{array}$

Conclusion:

Therefore, the area of the square is 288 square inches.