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 1
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.
a. Which board will Mia use for the length of the shelter, given that 1 foot =12 inches?
b. What is the width of the shelter, measured in feet?
c. 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?
Question 2
For the roof of the shelter, Mia has a board that measures 1 square yard, a second board that measures 3 feet, and a third board that measures 36 inches by 36 inches. Which of the boards, 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.
Question 1:
a. To determine which board Mia will use for the length of the shelter, we need to convert the length of the shelter from feet to inches.
Since 1 foot = 12 inches, the length of the shelter in inches would be 3.25 * 12 = 39 inches.
Comparing the lengths of the boards, we can see that the board measuring 39 inches is the one that matches the length of the shelter. Therefore, Mia will use the board measuring 39 inches for the length of the shelter.
b. To find the width of the shelter in feet, we need to convert the width from inches to feet.
Since 1 foot = 12 inches, the width of the shelter in feet would be 39 / 12 = 3.25 feet.
Therefore, the width of the shelter is 3.25 feet.
c. To find how many feet of board Mia needs to cut off the existing board to match the width of the shelter, we need to subtract the width of the shelter (in feet) from the length of the existing board (in feet).
The length of the existing board, converted to feet, would be 36 / 12 = 3 feet.
The amount of board Mia needs to cut off would be 3 - 3.25 = -0.25 feet.
Since Mia cannot cut off a negative amount, we can conclude that Mia doesn't need to cut off any part of the existing board to match the width of the shelter.
Question 2:
To determine whether any of the three boards will cover all the space needed for the roof, we need to determine the area of the roof in square feet and compare it to the areas of the boards.
The area of the roof can be calculated as the length (in feet) multiplied by the width (in feet) of the shelter.
Since the length of the shelter is 3.25 feet and the width of the shelter is also 3.25 feet (according to question 1), the area of the roof would be 3.25 * 3.25 = 10.5625 square feet.
Now let's compare this with the areas of the boards:
- The board measuring 1 square yard would cover an area of 1 square yard = 1 * 3 * 3 = 9 square feet. This is smaller than the roof area of 10.5625 square feet.
- The board measuring 3 feet would cover an area of 3 * 3 = 9 square feet. Again, this is smaller than the roof area.
- The third board measuring 36 inches by 36 inches would cover an area of 36 * 36 = 1296 square inches. To convert this to square feet, we divide by the conversion factor of 12 * 12 = 144. So the area in square feet would be 1296 / 144 = 9 square feet. Once again, this is smaller than the roof area.
Therefore, none of the three boards will cover all the space needed for the roof. Mia will need to find another board or a combination of boards to cover the entire roof area.