CONVERTING WITHIN A SYSTEM PORTFOLIO
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 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.
To determine if any of the given boards will cover all the space needed for the roof, we need to compare the total area of the roof to the area of each board.
First, let's convert all the measurements to the same unit. Since we are given both square yards and square feet, let's convert everything to square feet.
1 yard = 3 feet, so 1 square yard = (3 feet) * (3 feet) = 9 square feet.
Now let's compare the area of each board with the total area needed for the roof.
The board that measures 1 square yard = 9 square feet.
The board that measures 3 feet by 3 feet = (3 feet) * (3 feet) = 9 square feet.
The board that measures 36 inches by 36 inches = (36 inches) * (36 inches) = 1296 square inches. To convert square inches to square feet, we divide by 144 (since 1 square foot = 144 square inches). Therefore, the area in square feet is 1296 square inches / 144 = 9 square feet.
Since all three boards have an area of 9 square feet, any one of them will cover all the space needed for the roof.