Chapter 1.4, Problem 50E

Solution

To find: The value of $x$ when the side of a square is $2x$ and the area of the square is $36$ .

  $x=3$

Given information:

A square of side $2x$ and area $36$ .

Concept used:

Formula for the area of a square of side length $s$ is given as $\text{Area}=s^2$ .

Calculation:

The side of the given square is $2x$ . So, the area of the square is $\text{Area}={\left(2x\right)}^2$ .

The area of the square is given to be $36$ .

So, ${\left(2x\right)}^2=36$ .

Now, solve this equation as follows:

  $\begin{array}{c}{\left(2x\right)}^2=36\\ 4x^2=36\\ \frac{4x^2}{4}=\frac{36}{4}\\ x^2=9\\ x=\pm \sqrt{9}\\ x=\pm 3\end{array}$

Since the length cannot be negative, the value $x=-3$ is discarded. So, the value of $x$ is $3$ .

Conclusion:

The value of $x$ is $3$ .