Chapter 7.2, Problem 1P

To determine

To find: The value of x .

Answer to Problem 1P

The value of x is 1.65 m.

Explanation of Solution

Given:

The dimension of each side of the square = 4 m.

Calculation:

The area of the square is given by

  $\begin{array}{l}A=a^2\\ \text{Here, }a\text{is the side of the square}\text{.}\end{array}$

The initial area of the square

  $\begin{array}{l}{A}_1=4^2\\ A_1=16{\text{ m}}^2\end{array}$

Each side of the square is increased by x m. The area becomes double.

New area of the square becomes

  $\begin{array}{l}{A}_2={\left(4+x\right)}^2\\ A_2=2A_1\\ 2\times 16={\left(4+x\right)}^2\\ \left(4+x\right)=\sqrt{32}\\ x=4\sqrt{2}-4\\ x=4\left(\sqrt{2}-1\right)\\ x=1.65\text{ m}\end{array}$

Therefore, the value of x is 1.65 m.

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