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. 1 ft. = 13 yard.
Which of the boards, if any, will cover all the space needed for the roof? Explain your answer, drawing a picture as necessary.
To determine which board(s) will cover all the space needed for the roof, we need to compare the total area of the roof space to the area covered by each board.
To convert the measurements to a consistent unit, we first need to convert the second board's measurements from feet to yards. As given, 1 ft = 1/3 yard. So, the second board measures 3/3 yard by 3/3 yard, which simplifies to 1 yard by 1 yard.
Now, we can calculate the total area of the roof. Let's assume the roof space measures x yards in width and y yards in length. Therefore, the total area of the roof is x * y square yards.
For the first board, the area covered is 1 square yard, which is less than the total area of the roof unless x*y is equal to or less than 1 square yard.
For the second board, the area covered is 1 yard * 1 yard = 1 square yard. So, this board will cover the entire roof space if the total area is equal to or less than 1 square yard.
For the third board, the area covered is 36 inches * 36 inches = (36/36) yards * (36/36) yards = 1 square yard. This board will also cover the entire roof space if the total area is equal to or less than 1 square yard.
In summary, both the second and third boards will cover all the space needed for the roof if the total area is equal to or less than 1 square yard.