Imagine this: **a square garden has an area of 225 square feet the owner** wants to build a fence around it. How much fencing will they need? Sounds like a math problem, right? Don’t worry, it’s easier than it seems. Let’s break it down together! This article will guide you through calculating the side length of the square and the perimeter, answering the owner’s fencing question.
Understanding the Question
Let’s make sure we’re on the same page. The problem tells us the area of a square garden. Remember, the area is the space *inside* the shape. The owner wants to know how much fencing they need. Fencing goes *around* the garden. Therefore, we need to find the perimeter, the total length of all the sides.
Step-by-Step Solution: Finding the Fencing Needed for a Square Garden
Here’s how we solve it:
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Find the side length: We know the area of a square is calculated by side * side (or side squared, side²). We know the area is 225 square feet. So, we need to figure out what number, when multiplied by itself, equals 225. This is called finding the square root. The square root of 225 is 15. Each side of the garden is 15 feet long.
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Calculate the perimeter: The perimeter is the distance around the garden. A square has four equal sides. To find the perimeter, multiply the side length by 4: 15 feet * 4 = 60 feet.
Final Answer
The owner needs **60 feet** of fencing.
Why This Answer is Correct
We found the side length by using the area and square root and used that length to calculate the perimeter. We made sure to consider all four sides of the square garden.
Alternative Methods (If Applicable)
There isn’t a significantly different way to solve this basic perimeter calculation.
Common Mistakes
* **Forgetting the Square Root:** The most common error is forgetting to take the square root to find the side length.
* **Confusing Area and Perimeter:** Remember, the area is the space *inside* the shape, and the perimeter is the distance *around* it.
Conclusion
Finding the fencing needed for a square garden with an area of 225 square feet might seem tricky at first, but it is straightforward once you know the basics of squares, area, and perimeter. Remember to find the side length from the area and then calculate the perimeter. Well done!
FAQ
* **What if the garden wasn’t a perfect square?** If the garden was a rectangle, you’d need the length and width to calculate the perimeter. The formula would be 2 * (length + width).
* **How do you find the area of a square?** The area of a square is calculated by side * side (side²). If you know the side length, you can easily calculate the area.