Each square represents 625 square feet, each line segment represents 25 feet.
A galapagos tortoise must use 550 feet of fencing to enclose a space of 15,000.
What squares? What is your question?
24
To find the dimensions of the space the galapagos tortoise is trying to enclose, we can use the given information:
- Each square represents 625 square feet.
- Each line segment represents 25 feet.
- The tortoise must use 550 feet of fencing to enclose the space.
- The space to be enclosed is 15,000 square feet.
First, let's find the total area of the space to be enclosed using the given information. Since each square represents 625 square feet, we divide the total area by 625:
15,000 square feet / 625 square feet = 24 squares.
So, the total area can be represented by 24 squares.
Now, let's find the total length of the fencing required. Since each line segment represents 25 feet, we divide the total length of fencing by 25:
550 feet / 25 feet = 22 line segments.
So, the total length of fencing required can be represented by 22 line segments.
To find the dimensions of the space, we need to determine the length and width of the rectangular enclosure. We know that the total area is 24 squares, so we need to find the factors of 24 that allow us to calculate the length and width.
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
We can try each factor to find the best combination that matches the given information. Let's go through the factors:
- For a factor of 1, we would have a length of 24 squares and a width of 24 squares, which would require more fencing than 550 feet.
- For a factor of 2, we would have a length of 12 squares and a width of 24 squares, which would require 36 squares of fencing (2 × 12 + 2 × 24 = 72 squares) and exceed the available 550 feet.
- For a factor of 3, we would have a length of 8 squares and a width of 24 squares, which would require 56 squares of fencing (2 × 8 + 2 × 24 = 64 squares) and be below the available 550 feet.
- For a factor of 4, we would have a length of 6 squares and a width of 24 squares, which would require 52 squares of fencing (2 × 6 + 2 × 24 = 60 squares) and be below the available 550 feet.
- For a factor of 6, we would have a length of 4 squares and a width of 24 squares, which would require 48 squares of fencing (2 × 4 + 2 × 24 = 56 squares) and be below the available 550 feet.
- For a factor of 8, we would have a length of 3 squares and a width of 24 squares, which would require 50 squares of fencing (2 × 3 + 2 × 24 = 54 squares) and exceed the available 550 feet.
- For a factor of 12, we would have a length of 2 squares and a width of 24 squares, which would require 52 squares of fencing (2 × 2 + 2 × 24 = 52 squares) and match the available 550 feet.
- For a factor of 24, we would have a length of 1 square and a width of 24 squares, which would require 50 squares of fencing (2 × 1 + 2 × 24 = 50 squares) and be below the available 550 feet.
Therefore, the best combination is a length of 2 squares and a width of 24 squares, which requires 52 squares of fencing (2 × 2 + 2 × 24 = 52 squares) and matches the available 550 feet.
To summarize, the dimensions of the space to be enclosed by the galapagos tortoise are:
- Length = 2 squares (or 2 × 25 feet = 50 feet)
- Width = 24 squares (or 24 × 25 feet = 600 feet)
Note: The given information and calculations were based on the assumption that the space to be enclosed is a rectangular shape.