Using proportional relationships. 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. Show your work.

Question

Question 1. Mia will use one of these boards for the length of the shelter. She knows she wants the length of shelter to measure 3.25 feet. She will use a different board for the width of the shelter. Thw 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?
What is the width of the shelter,measured in feet?
Mia needs to cut the third board to match the width of the shelter. How many feet of the board will she need to cut off the existing board to reach this goal?
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 ,if any of these ,will cover all the space needed for the roof? Explain your answer, drawing a picture if necessary. 1 foot= 1/3 of a yard.

Answer 1

Let's solve Mia's shelter problem step-by-step.

Question 1:

1. Determine the Length of the Shelter:

   Mia wants the length of the shelter to be 3.25 feet. We will first convert this to inches: \[ 3.25 \text{ feet} = 3.25 \times 12 \text{ inches} = 39 \text{ inches} \]

   Now, we compare this length to the available boards:

   • 36 inches
   • 39 inches
   • 42 inches

   Since 39 inches matches one of the available boards exactly, Mia will use the 39-inch board for the length of the shelter.

2. Determine the Width of the Shelter:

   The width of the shelter needs to be shorter than the length (39 inches). We will determine an appropriate width considering the boards available. The possible widths from the other boards are 36 inches and 42 inches. Since the width must be less than 39 inches, Mia can only use the 36-inch board.

   Now, we convert the width to feet: \[ 36 \text{ inches} = \frac{36}{12} = 3 \text{ feet} \]

3. Cutting the Third Board:

   Mia needs to cut the third board (42 inches) to match the width of the shelter (36 inches). To find out how much she needs to cut off: \[ 42 \text{ inches} - 36 \text{ inches} = 6 \text{ inches} \]

   In feet, this is: \[ \frac{6 \text{ inches}}{12} = 0.5 \text{ feet} \]

   Therefore, Mia needs to cut off 6 inches (or 0.5 feet) from the 42-inch board.

Question 2:

Now, let's determine if any of the boards will cover the roof space needed.

1. Convert the Boards for the Roof:

   • First board: 1 square yard \[ 1 \text{ square yard} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet} \]
   • Second board: 3 feet by 3 feet \[ \text{Area} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet} \]
   • Third board: 36 inches by 36 inches \[ 36 \text{ inches} = 3 \text{ feet} \] \[ \text{Area} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet} \]

2. Conclusion:

   All three options (1 square yard, the board measuring 3 feet by 3 feet, and the board measuring 36 inches by 36 inches) have an area of 9 square feet.

   Therefore, all of these boards will cover the roof space needed for the shelter, as they all have the same area of 9 square feet.

Summary:

1. Mia will use the 39-inch board for the length, and the width will be 3 feet (36 inches). She needs to cut off 6 inches (0.5 feet) from the 42-inch board.
2. All boards (1 square yard, 3 feet by 3 feet, and 36 inches by 36 inches) will cover the roof space adequately.