To address the questions provided step by step:
Question 1a:
Mia wants the length of the shelter to be 3.25 feet. First, we need to convert 3.25 feet into inches since the board lengths are given in inches.
\[ 3.25 \text{ feet} \times 12 \text{ inches/foot} = 39 \text{ inches} \]
Now, looking at the available boards:
- Board 1 = 36 inches
- Board 2 = 39 inches
- Board 3 = 42 inches
Since the length of the shelter needs to be 39 inches, Mia will select:
Board 2 that measures 39 inches.
Question 1b:
The width of the shelter needs to be shorter than the length (39 inches). For simplicity, let's assume an appropriate width could be 36 inches or less. However, since we need the width in feet:
The width could be any value less than 3.25 feet which Mia can determine based on the board lengths available.
The width of the shelter can be:
3 feet (which is shorter than 3.25 feet).
Question 1c:
Now, Mia needs to cut the third board (which is 42 inches) to match the width of the shelter (which is 36 inches).
Mia will need to cut:
\[ 42 \text{ inches} - 36 \text{ inches} = 6 \text{ inches} \]
To express this in feet:
\[ 6 \text{ inches} \div 12 \text{ inches/foot} = 0.5 \text{ feet} \]
Mia needs to cut off:
6 inches or 0.5 feet.
Question 1d:
Now, we check which board can cover the roof of the shelter:
- 1 square yard = 3 feet x 3 feet = 9 square feet.
- 3 feet by 3 feet = 9 square feet.
- 36 inches by 36 inches = 3 feet x 3 feet = 9 square feet.
Mia's shelter has an area of 39 inches (3.25 feet) in length and 36 inches (3 feet) in width, which overall would require covering with boards totaling an area of:
\[ 3.25 \text{ ft} \times 3 \text{ ft} = 9.75 \text{ square feet} \]
So, the boards available:
- The first two options cover 9 square feet, and the last option (36 inches x 36 inches) also covers 9 square feet.
None of these boards cover the entire required area of 9.75 square feet alone.
Therefore, the answer would be:
None of these boards will work.
1 answer