For the roof of the shelter, Mia has a board that measures 1 square yard, a second board that measured 3 feet by 3 feet, and a third board that measures 36 inches by 36 inches. 1ft. =1/3 yard.
Which of the Boards,if any, will cover all the space needed for the roof?
Explain your answer, drawing a pictures as necessary.
None of the boards will cover all the space needed for the roof. The first board measures 1 square yard, the second board measures 9 square feet, and the third board measures 16 square feet. In total, this is only 26 square feet, which is not enough to cover the space needed for the roof.
To illustrate this, imagine a square with an area of 36 square feet. The first board would cover 1/3 of the square, the second board would cover 1/4 of the square, and the third board would cover 1/2 of the square. This would leave 1/12 of the square uncovered.
Therefore, none of the boards will cover all the space needed for the roof.
Picture:
[Insert Picture Here]
To determine which board, if any, will cover all the space needed for the roof, we need to compare the dimensions of each board to the required area.
First, let's convert the measurements to a consistent unit. Given that 1ft = 1/3 yard, we can convert the measurements as follows:
- 3 feet by 3 feet board: 3ft × 1/3yd/ft = 1 yard by 1 yard.
- 36 inches by 36 inches board: 36in × 1/36yd/in = 1 yard by 1 yard.
Now that all the dimensions are in yards, we can compare the areas.
1. The first board measures 1 square yard. This means it covers an area of 1 yard by 1 yard, which is equal to 1 square yard.
2. The second board measures 1 yard by 1 yard. Hence, it covers an area of 1 square yard.
3. The third board also measures 1 yard by 1 yard, so it covers an area of 1 square yard.
Therefore, all three boards have the same area of 1 square yard, and any of them can cover the entire space needed for the roof.
To determine which board, if any, will cover all the space needed for the roof, we need to convert all the measurements to a consistent unit. Since 1ft = 1/3 yard, we can convert all measurements to yards.
1 square yard is already in yards.
To convert the second board, which measures 3 feet by 3 feet, to yards, we can divide each side by 3. So 3 feet = 1 yard.
To convert the third board, which measures 36 inches by 36 inches, to yards, we can divide each side by 36 (since there are 36 inches in 1 yard). So 36 inches = 1 yard.
Now, let's compare the measurements:
Board 1: 1 square yard
Board 2: 1 yard by 1 yard
Board 3: 1 yard by 1 yard
From the measurements, we can see that all three boards are the same size, measuring 1 yard by 1 yard. Therefore, any of the three boards will cover all the space needed for the roof.
Here is a diagram to help visualize the measurements:
```
Board 1: 1 square yard
------- (1 yard)
| |
| 1 |
| |
Board 2: 1 yard by 1 yard
------- (1 yard)
| |
| 1 |
| |
Board 3: 1 yard by 1 yard
------- (1 yard)
| |
| 1 |
| |
```
As you can see, all three boards have the same dimensions and can cover the entire roof space.