Question 1: Mia is building a three-sided shelter for her action figures. The shelter will resemble a rectangle with one of the long sides removed. She has boards that measure 36 inches, 39 inches, and 42 inches in length; all the boards are the same width. Mia will need to convert some of these measurements into other imperial units to build the shelter the way she wants. Answer the following questions using this information. Be sure to work out your problems on paper and use a calculator if needed. 1a. Mia will use one of these boards for the length of the shelter. She knows she wants the length of the shelter to measure 3.25 feet. She will use a different board for the width of the shelter. The width of the shelter will be shorter than the length. Which board will Mia use for the length of the shelter, given that 1 foot = 12 inches? (2 points) Responses Board 1 that measures 36 inches Board 1 that measures 36 inches Board 2 that measures 39 inches Board 2 that measures 39 inches Board 3 that measures 42 Board 3 that measures 42 Question 2 1b. Use the information from question 1a to solve this question. What is the width of the shelter, measured in FEET? *Remember the width will be shorter than the length. (2 points) Responses 3 feet 3 feet 3.25 feet 3.25 feet 3.5 feet 3.5 feet Question 3 1c. Mia needs to cut the third board to match the width of the shelter. How many feet of board will she need to cut off the existing board to reach this goal? (2 points) Responses 6 inches or 0.5 feet 6 inches or 0.5 feet 3 inches or 0.25 feet 3 inches or 0.25 feet 12 inches or 1 foot 12 inches or 1 foot Question 4 1d. 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? 1 foot = 1/3 of a yard (2 points) Responses The board measuring 1 square yard The board measuring 1 square yard The board measuring 3 feet by 3 feet The board measuring 3 feet by 3 feet The board measuring 36 inches by 36 inches The board measuring 36 inches by 36 inches None of these boards will work

To answer the questions related to Mia's shelter, let's go through them 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 provided 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 39 inches matches the desired length of 3.25 feet, Mia will use Board 2 that measures 39 inches for the length of the shelter.

Question 2 1b:

The width of the shelter must be shorter than the length (39 inches). Among the available boards, the only board shorter than 39 inches is Board 1, which measures 36 inches.

To convert the width from inches back to feet: \[ 36 , \text{inches} \div 12 , \text{inches/foot} = 3 , \text{feet} \]

Thus, the width of the shelter is 3 feet.

Question 3 1c:

Mia needs to cut the width of the shelter from the third board, which could be Board 3 (42 inches). The desired width is 36 inches.

To calculate how much needs to be cut off: \[ 42 , \text{inches} - 36 , \text{inches} = 6 , \text{inches} \]

Converting inches into feet: \[ 6 , \text{inches} \div 12 , \text{inches/foot} = 0.5 , \text{feet} \]

Hence, Mia needs to cut off 6 inches or 0.5 feet from the existing board.

Question 4 1d:

For the roof, we will compare the area of the boards with the area needed for the roof.

1. Board that measures 1 square yard: \[ 1 , \text{square yard} = 3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet} \]

2. Board that measures 3 feet by 3 feet: \[ 3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet} \]

3. Board that measures 36 inches by 36 inches: \[ 36 , \text{inches} = 36 \div 12 = 3 , \text{feet} \] \[ 3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet} \]

All three boards measure 9 square feet, which is sufficient to cover the roof. Therefore, each of the boards (the board measuring 1 square yard, the board measuring 3 feet by 3 feet, and the board measuring 36 inches by 36 inches) will cover all the space needed for the roof.

Summary of Answers:

1. Length of shelter: Board 2 that measures 39 inches
2. Width of shelter: 3 feet
3. Board to cut: 6 inches or 0.5 feet
4. Roof covering: Each of the boards (1 square yard, 3 feet by 3 feet, 36 inches by 36 inches) will work.

Let's carefully re-evaluate the last question (1d) regarding the board dimensions needed for the roof based on Mia’s shelter structure.

Area Calculation

Since we established the width of the shelter to be 3 feet and the length to be 3.25 feet, we should first calculate the area of the roof required for the shelter:

1. Area of the Shelter Roof: \[ \text{Area} = \text{Length} \times \text{Width} \] \[ \text{Area} = 3.25 , \text{feet} \times 3 , \text{feet} = 9.75 , \text{square feet} \]

Assessment of Available Boards

Now, let’s assess the boards available for the roof:

1. Board that measures 1 square yard:

   • Area = 1 square yard = \(3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet}\)

2. Board that measures 3 feet by 3 feet:

   • Area = \(3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet}\)

3. Board that measures 36 inches by 36 inches:

   • Convert to feet: \(36 , \text{inches} = 3 , \text{feet}\)
   • Area = \(3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet}\)

Conclusion

All three boards measure 9 square feet. The required area for the roof is 9.75 square feet. Since none of the boards provide sufficient coverage (since 9 square feet is less than 9.75 square feet), none of these boards will work to entirely cover the roof of the shelter.

Correct Answer:

• None of these boards will work.

Thank you for your patience, and I apologize for the confusion in my earlier response!