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. Record your answers below.
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.
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
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 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
Question 1:
To find out which board Mia will use for the length of the shelter, we can convert the length she wants (3.25 feet) into inches. Since 1 foot is equal to 12 inches, we can multiply 3.25 by 12 to get the length in inches:
3.25 feet * 12 inches/foot = 39 inches
Therefore, Mia will use the board that measures 39 inches for the length of the shelter.
To find the width of the shelter in feet, we need to determine the length of the other board. Since the width is shorter than the length, we can check which of the given boards has a length less than 39 inches. In this case, the board that measures 36 inches is the only one that meets this requirement.
To convert 36 inches to feet, we divide by 12:
36 inches / 12 inches/foot = 3 feet
Therefore, the width of the shelter is 3 feet.
To find out how many feet of board Mia needs to cut off the existing board to match the width of the shelter, we subtract the desired width (3 feet) from the original length of the board (36 inches) after converting it to feet:
36 inches / 12 inches/foot - 3 feet = 0 feet
Since the original length of the board is already equal to the desired width of the shelter, Mia does not need to cut off any board for this goal.
Question 2:
To determine if any of the given boards will cover all the space needed for the roof, we need to compare the area of each board to the total area needed for the roof.
The first board measures 1 square yard, which is equal to an area of 1 yard * 1 yard = 1 square yard.
The second board measures 3 feet * 3 feet = 9 square feet.
The third board measures 36 inches * 36 inches = 1296 square inches. To convert this to square feet, we divide by 12 * 12 (since there are 12 inches in a foot):
1296 square inches / (12 inches/foot * 12 inches/foot) = 9 square feet
Comparing the areas, we see that both the second board and the third board can cover all the space needed for the roof, as both have an area of 9 square feet.
Therefore, both the second board (measuring 3 feet by 3 feet) and the third board (measuring 36 inches by 36 inches) will cover all the space needed for the roof.