I have a math question that I am somewhat confused on that I need a bit of help with please.
What is the shortest possible perimeter for an arrangement with an area of 15 square feet?
How do I go about figuring this out?
Is it a multiple choice or do you write it out?
Good morning,
Unfortunately there is no multiple choice
To find the shortest possible perimeter for an arrangement with an area of 15 square feet, we first need to understand the concept of perimeter and area.
The perimeter is the distance around the outside of a shape, while the area is the measure of the space inside the shape.
To find the shortest possible perimeter, we need to consider the different possible arrangements that can form a shape with an area of 15 square feet.
One of the most common shapes with a given area is a rectangle. The formula to calculate the area of a rectangle is length multiplied by width: Area = length × width.
In this case, we are given that the area is 15 square feet. Therefore, we can write the equation: 15 = length × width.
Now, we need to find the minimum perimeter. The perimeter of a rectangle is calculated by adding the lengths of all four sides together: Perimeter = 2(length + width).
To minimize the perimeter, we can start by assuming that the length and width are equal, making it a square. In this case, the equation becomes 15 = side length × side length, or simply 15 = side length².
To find the side length, we can take the square root of both sides of the equation: √15 = side length.
By simplifying the square root of 15, we get approximately side length ≈ 3.87 feet.
Therefore, if the side length is approximately 3.87 feet, the dimensions of the rectangle are length ≈ 3.87 feet and width ≈ 3.87 feet. The perimeter, in this case, would be approximately 15.48 feet (2 × (3.87 + 3.87)).
In conclusion, the shortest possible perimeter for an arrangement with an area of 15 square feet is approximately 15.48 feet when considering a square arrangement.