The director of the center has asked you to design a garden. The director has asked you to design different sections of the garden that meet the following:
Section 1 must be shaped like a square.
Section 1 must have an area between 26 square feet and 50 square feet.
section 2 must be shaped like a rectangle but not a square.
section 2 must be exactly twice the area of section 1.
Put this in a grid.
Section 1 can be either 36 or 49 sq. ft. Choose one and then work for Section 2.
We cannot put a grid on this post.
To design the garden with the given requirements, we need to follow these steps:
Step 1: Determine the possible areas for Section 1.
Section 1 needs to be shaped like a square and have an area between 26 and 50 square feet. We need to find square numbers within this range. We can start by finding the square root of the lower and upper limits.
The square root of 26 is approximately 5.1, and the square root of 50 is approximately 7.1. We can round these values up to the nearest whole number to get the possible side lengths for Section 1. So, the side length of Section 1 can be 6 or 7 feet.
Next, we calculate the area of each possible side length:
- If Section 1 has a side length of 6 feet, then the area would be 6 x 6 = 36 square feet.
- If Section 1 has a side length of 7 feet, then the area would be 7 x 7 = 49 square feet.
Therefore, Section 1 can have an area of either 36 square feet or 49 square feet.
Step 2: Determine the dimensions of Section 2.
Section 2 needs to be shaped like a rectangle but not a square. It should have an area exactly twice that of Section 1.
Since Section 1 can have an area of either 36 or 49 square feet, we need Section 2 to have an area of 2 times either 36 or 49 square feet.
If Section 1 has an area of 36 square feet:
- The area of Section 2 needs to be 2 x 36 = 72 square feet.
To find the length and width of the rectangle, let's list all possible pairs of numbers that multiply to 72:
(1, 72), (2, 36), (3, 24), (4, 18), (6, 12), and (8, 9).
Since Section 2 should not be shaped like a square, we can eliminate pairs with equal dimensions. From the remaining pairs, we can choose any that fulfill the requirement of Section 2 being a rectangle but not a square. Let's choose (6, 12) as the dimensions for Section 2.
If Section 1 has an area of 49 square feet:
- The area of Section 2 needs to be 2 x 49 = 98 square feet.
Listing all possible pairs of numbers that multiply to 98:
(1, 98), (2, 49), (7, 14).
Again, we choose (7, 14) as the dimensions for Section 2 because it is a rectangle but not a square.
Step 3: Arrange the sections in a grid.
Now that we have the dimensions for the sections, we can represent them in a grid.
Using "S" to represent Section 1 and "L" to represent Section 2, the garden layout can be as follows:
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| S | L | |
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| L | | |
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| | | |
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Note that the placement of the sections in the grid can be adjusted based on your preference and the available space.