Question 2
For the roof of the shelter, Mia has a board that measures 1 square yard, a second
board that measures 3 feet by 3 feet, and a third board that measures 36 inches by
36 inches. Which of these, if any, will cover all the space needed for the roof?
Explain your answer, drawing a picture if necessary.
1 foot = 1/3 of a yard
To compare the sizes of the three boards Mia has, we'll convert each measurement to the same units. Since two of the boards are provided in feet and inches, it's easiest to convert all measurements to feet.
Board 1: 1 square yard
1 yard is equivalent to 3 feet. Therefore, 1 square yard is equivalent to a board that is 3 feet by 3 feet.
Board 2: 3 feet by 3 feet
This board is already in feet, so we don't need to convert anything.
Board 3: 36 inches by 36 inches
There are 12 inches in a foot. Therefore, 36 inches is equivalent to 36/12 = 3 feet. The dimensions in feet would be 3 feet by 3 feet.
From the above conversions, we see that all three boards are actually the same size in terms of area, since they all convert to 3 feet by 3 feet. Each board, therefore, has an area of:
Area = 3 feet * 3 feet = 9 square feet
Since all boards have the same dimensions, any of the three boards will cover the same amount of space for the roof. Without specific measurements for the shelter's roof, we can't determine whether 9 square feet (the area of each board) will cover the entire space needed for the roof. However, based on the information given, any of the boards would provide the same coverage as they are all the same size once converted to the same units of measurement.
Here's a simple representation of the boards:
```
Board 1: Board 2: Board 3:
+---------+ +---------+ +---------+
| | | | | |
| | | | | |
| 3 ft | | 3 ft | | 3 ft |
| | | | | |
| | | | | |
+---------+ +---------+ +---------+
3 ft 3 ft 3 ft
```
In conclusion, any of the three boards is capable of covering the same square footage for the roof, as they all translate to a board that measures 3 feet by 3 feet. To make a final decision on which board to use, Mia would need to consider the measurements of the shelter's roof, which are not provided in this scenario.