Question

HELPP Natasha is eating her backyard. The backyard is square in shape and has an area of 4,096 feet. What is a length of one side of Natasha's backyard?

Answer 1

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:

`\text{Side of a square = x}`

We will now express the Area of the square in terms of its side length using the basic definition as follows:

`\text{Area of square = Length}^2`

We will now express the above in terms of the side length variable ( x ) as follows:

`\text{Area of square = x}^2`

We are given that Natasha's garden has the following area:

`\text{Area of square = 4096 ft}^2`

Now we will equate the result of area of a square with the side length ( x ) terms as follows:

`4096=x^2`

Evaluate(solve) the above the equation for the variable ( x ) by taking a square root on both sides of the equation as follows:

`\begin{gathered} √(x^2)\text{ = }√(4096) \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{=}\text{\textcolor{#FF7968}{ }}\textcolor{#FF7968}{\pm}\text{\textcolor{#FF7968}{ 64}} \end{gathered}`

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:

`\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 64 feet}}`