A farmer wants to fence a square plot with an area of [tex]$400 ft^2$[/tex]. What is the length of any side?
Answer (2)
The problem gives the area of a square plot as 400 f e s 2 and asks for the length of one side.
We use the formula for the area of a square, A re a = s 2 , where s is the side length.
We set up the equation s 2 = 400 .
Solving for s , we find s = 400 = 20 .
The length of one side of the square plot is 20 .
Explanation
Problem Analysis The problem states that a farmer has a square plot with an area of 400 f e s 2 (fes is assumed to be feet). The objective is to find the length of one side of this square plot.
Area Formula Let s be the length of one side of the square plot. The area of a square is given by the formula: A re a = s 2
Setting up the equation We are given that the area is 400 f e s 2 , so we have the equation: s 2 = 400
Solving for side length To solve for s , we take the square root of both sides of the equation: s = 400 s = 20
Final Answer Since the side length must be positive, we take the positive square root. Therefore, the length of one side of the square plot is 20 feet.
Examples
Understanding area and side lengths of squares is useful in many real-world scenarios. For example, when planning a garden, you might know the total area you want to use and need to determine the dimensions of a square plot. Similarly, if you're tiling a square floor, knowing the area helps you calculate the length of each side, which is essential for buying the right amount of materials. This concept is also used in construction and land surveying to determine property boundaries and land sizes.
The length of one side of a square plot with an area of 400 square feet is 20 feet. This is found by using the area formula A re a = s 2 and solving s 2 = 400 . Taking the square root yields s = 20 .
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