The scale drawing of the rectangular classroom floor has dimensions of 8 inches by 5 inches. The actual length of the longer side of the floor is 32 feet.
What is the actual area of the floor in square feet?
(2 points)
• 40 feet?
• 240 feet?
• 640 feet?
O 92,160 feet?
Show your work for this problem. Be sure to show each step and explain using math vocabulary.
To find the actual area of the floor in square feet, we first need to find the scale factor between the scale drawing and the actual dimensions of the room.
Given:
Scale drawing dimensions: 8 inches by 5 inches
Actual longer side: 32 feet
We first need to convert the scale drawing dimensions to feet:
1 inch = 1/12 feet
Scale drawing dimensions:
8 inches = 8/12 feet = 2/3 feet
5 inches = 5/12 feet
Scale factor for the longer side:
32 feet / (2/3 feet) = 32 / 2/3 = 32 * 3/2 = 96/2 = 48
Now, we find the actual dimensions of the room:
Longer side: 32 feet
Shorter side: 48 * (5/12) = 48 * 5/12 = 20 feet
Now we can find the actual area of the room:
Area = length * width
Area = 32 feet * 20 feet
Area = 640 square feet
Therefore, the actual area of the floor is 640 square feet. The correct option is:
• 640 feet