Given the area of a square is 225 square feet, what is the length of each side?
The Correct Answer and Explanation is:
To determine the length of each side of a square when given its area, we can use the formula for the area of a square:
[
\text{Area} = \text{side}^2
]
Here, the area is provided as 225 square feet. Let’s represent the length of each side as ( s ). According to the formula, we have:
[
s^2 = 225
]
To find ( s ), we need to take the square root of both sides:
[
s = \sqrt{225}
]
Calculating the square root of 225, we get:
[
s = 15
]
Therefore, the length of each side of the square is 15 feet.
Explanation
A square is a geometric shape with four equal sides and four right angles. Its area, which is the amount of space it covers, can be calculated by squaring the length of one side. This is because the formula for the area of a square is derived from multiplying the side length by itself (side × side). When given the area of a square and asked to find the side length, we reverse the process by taking the square root.
In this example, the area of the square is 225 square feet. To find the side length, we set up the equation ( s^2 = 225 ), where ( s ) represents the length of each side. Solving for ( s ) by taking the square root of both sides, we find that ( s = 15 ) feet.
Understanding this method is useful in many applications where you know the area but need to determine the dimensions. For instance, this calculation might apply in fields such as construction, landscaping, or interior design, where determining lengths from areas can help in planning and resource allocation.