Answer :
Sure! Let's find the actual dimensions and area of the room given the scale and drawing measurements.
Step 1: Understand the Scale
The scale of the drawing is 64 inches to 1 inch. This means that every inch on the drawing represents 64 inches in real life.
Step 2: Convert the Drawing Measurements to Real-Life Dimensions
- The length of the room on the drawing is [tex]\(2 \frac{3}{4}\)[/tex] inches. Let's convert this to a decimal:
- [tex]\(2 \frac{3}{4} = 2 + \frac{3}{4} = 2.75\)[/tex] inches.
- The width of the room on the drawing is [tex]\(2 \frac{5}{8}\)[/tex] inches. Let's convert this to a decimal as well:
- [tex]\(2 \frac{5}{8} = 2 + \frac{5}{8} = 2.625\)[/tex] inches.
Now, use the scale to find the real-life dimensions:
- Real-life length = [tex]\(2.75 \times 64\)[/tex] inches.
- Real-life width = [tex]\(2.625 \times 64\)[/tex] inches.
Step 3: Convert Inches to Feet
Since there are 12 inches in a foot, we can convert these measurements to feet:
- Real-life length in feet = [tex]\(\frac{2.75 \times 64}{12}\)[/tex].
- Real-life width in feet = [tex]\(\frac{2.625 \times 64}{12}\)[/tex].
After performing these calculations, the actual dimensions are approximately:
- Actual length = [tex]\(176.0\)[/tex] feet
- Actual width = [tex]\(168.0\)[/tex] feet
Step 4: Calculate the Area
The area of the room in square feet is calculated by multiplying the length and the width:
- Area = [tex]\(176.0 \,\text{feet} \times 168.0 \,\text{feet} = 29,568.0\)[/tex] square feet.
The actual dimensions of the room would be 176.0 feet by 168.0 feet, and the area would be 29,568.0 square feet.
Step 1: Understand the Scale
The scale of the drawing is 64 inches to 1 inch. This means that every inch on the drawing represents 64 inches in real life.
Step 2: Convert the Drawing Measurements to Real-Life Dimensions
- The length of the room on the drawing is [tex]\(2 \frac{3}{4}\)[/tex] inches. Let's convert this to a decimal:
- [tex]\(2 \frac{3}{4} = 2 + \frac{3}{4} = 2.75\)[/tex] inches.
- The width of the room on the drawing is [tex]\(2 \frac{5}{8}\)[/tex] inches. Let's convert this to a decimal as well:
- [tex]\(2 \frac{5}{8} = 2 + \frac{5}{8} = 2.625\)[/tex] inches.
Now, use the scale to find the real-life dimensions:
- Real-life length = [tex]\(2.75 \times 64\)[/tex] inches.
- Real-life width = [tex]\(2.625 \times 64\)[/tex] inches.
Step 3: Convert Inches to Feet
Since there are 12 inches in a foot, we can convert these measurements to feet:
- Real-life length in feet = [tex]\(\frac{2.75 \times 64}{12}\)[/tex].
- Real-life width in feet = [tex]\(\frac{2.625 \times 64}{12}\)[/tex].
After performing these calculations, the actual dimensions are approximately:
- Actual length = [tex]\(176.0\)[/tex] feet
- Actual width = [tex]\(168.0\)[/tex] feet
Step 4: Calculate the Area
The area of the room in square feet is calculated by multiplying the length and the width:
- Area = [tex]\(176.0 \,\text{feet} \times 168.0 \,\text{feet} = 29,568.0\)[/tex] square feet.
The actual dimensions of the room would be 176.0 feet by 168.0 feet, and the area would be 29,568.0 square feet.
