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Answer :
To determine which of the measurements are approximately equivalent to the perimeter of the bedroom (42 feet), we need to convert 42 feet into each of the units provided and check which ones match.
1. Convert feet to yards:
- Since 1 yard is equal to 3 feet, divide the perimeter in feet by 3.
- [tex]\( \text{Yards} = \frac{42}{3} = 14 \)[/tex] yards.
2. Convert feet to inches:
- Since 1 foot is equal to 12 inches, multiply the perimeter in feet by 12.
- [tex]\( \text{Inches} = 42 \times 12 = 504 \)[/tex] inches.
3. Convert feet to meters:
- Since 1 foot is approximately 0.3048 meters, multiply the perimeter in feet by 0.3048.
- [tex]\( \text{Meters} = 42 \times 0.3048 = 12.8016 \)[/tex] meters.
4. Convert feet to kilometers:
- Since 1 foot is approximately 0.0003048 kilometers, multiply the perimeter in feet by 0.0003048.
- [tex]\( \text{Kilometers} = 42 \times 0.0003048 = 0.0128016 \)[/tex] kilometers.
5. Convert feet to centimeters:
- Since 1 foot is equal to 30.48 centimeters, multiply the perimeter in feet by 30.48.
- [tex]\( \text{Centimeters} = 42 \times 30.48 = 1280.16 \)[/tex] centimeters.
Let’s match these converted values to the given choices:
- 126 yards: The perimeter is 14 yards, not 126 yards. This does not match.
- 3.5 inches: The perimeter is 504 inches, not 3.5 inches. This does not match.
- 12.8 meters: The calculated value is 12.8016 meters. Since 12.8 meters is approximately close, this can be considered a match.
- 0.01 kilometers: The perimeter is 0.0128016 kilometers, not 0.01 kilometers. This does not match.
- 1280.16 centimeters: The calculated perimeter is 1280.16 centimeters, which matches exactly.
Therefore, the measurements equivalent to the perimeter of the bedroom are:
- 12.8 meters (approximately)
- 1280.16 centimeters
1. Convert feet to yards:
- Since 1 yard is equal to 3 feet, divide the perimeter in feet by 3.
- [tex]\( \text{Yards} = \frac{42}{3} = 14 \)[/tex] yards.
2. Convert feet to inches:
- Since 1 foot is equal to 12 inches, multiply the perimeter in feet by 12.
- [tex]\( \text{Inches} = 42 \times 12 = 504 \)[/tex] inches.
3. Convert feet to meters:
- Since 1 foot is approximately 0.3048 meters, multiply the perimeter in feet by 0.3048.
- [tex]\( \text{Meters} = 42 \times 0.3048 = 12.8016 \)[/tex] meters.
4. Convert feet to kilometers:
- Since 1 foot is approximately 0.0003048 kilometers, multiply the perimeter in feet by 0.0003048.
- [tex]\( \text{Kilometers} = 42 \times 0.0003048 = 0.0128016 \)[/tex] kilometers.
5. Convert feet to centimeters:
- Since 1 foot is equal to 30.48 centimeters, multiply the perimeter in feet by 30.48.
- [tex]\( \text{Centimeters} = 42 \times 30.48 = 1280.16 \)[/tex] centimeters.
Let’s match these converted values to the given choices:
- 126 yards: The perimeter is 14 yards, not 126 yards. This does not match.
- 3.5 inches: The perimeter is 504 inches, not 3.5 inches. This does not match.
- 12.8 meters: The calculated value is 12.8016 meters. Since 12.8 meters is approximately close, this can be considered a match.
- 0.01 kilometers: The perimeter is 0.0128016 kilometers, not 0.01 kilometers. This does not match.
- 1280.16 centimeters: The calculated perimeter is 1280.16 centimeters, which matches exactly.
Therefore, the measurements equivalent to the perimeter of the bedroom are:
- 12.8 meters (approximately)
- 1280.16 centimeters
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