We will determine how to evaluate the side length of a square given its area.
A square is a four sided 2D planar figure with all its sides at right angles and equal in magnitude as follows:
The side a square are all equal and will be denoted by a variable as follows:
[tex]\text{Side of a square = x}[/tex]We will now express the Area of the square in terms of its side length using the basic definition as follows:
[tex]\text{Area of square = Length}^2[/tex]We will now express the above in terms of the side length variable ( x ) as follows:
[tex]\text{Area of square = x}^2[/tex]We are given that Natasha's garden has the following area:
[tex]\text{Area of square = 4096 ft}^2[/tex]Now we will equate the result of area of a square with the side length ( x ) terms as follows:
[tex]4096=x^2[/tex]Evaluate(solve) the above the equation for the variable ( x ) by taking a square root on both sides of the equation as follows:
[tex]\begin{gathered} \sqrt{x^2}\text{ = }\sqrt{4096} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{=}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{\pm}\text{\textcolor{#FF7968}{ 64}} \end{gathered}[/tex]For practical sense, the variable ( x ) denotes the magnitude of the side length of the square which can not be negative. Hence, we have only solution for the side length ( x ) as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 64 feet}}[/tex]
