Final answer:
The longest zip line that can fit into a rectangular frame is found using the three-dimensional Pythagorean theorem, which for dimensions of 10 feet by 12 feet by 60 feet gives approximately 62.0 feet for the diagonal. The option closest to this calculation is 62.2 feet.
Option b is correct.
Step-by-step explanation:
The student is asking for the length of the longest zip line that can fit into a rectangular wooden frame with dimensions of 10 feet by 12 feet by 60 feet.
To find the length of the diagonal AC, which represents the zip line, we need to use the Pythagorean theorem in three dimensions.
This theorem states that the diagonal of a rectangular solid is the square root of the sum of the squares of the length, width, and height. Therefore, the calculation will be:
√(10² + 12² + 60²)
√(100 + 144 + 3600)
√(3844)
The square root of 3844, to the nearest tenth of a foot, is approximately 62.0 feet. Hence, the length of AC, the longest zip line, is 62.0 feet. But among the given options, the closest to 62.0 feet is option B. 62.2 feet.
When you measure dimensions, you have to choose the most appropriate unit for the task at hand.
For large objects like trees and frames, feet is the most suitable unit, while smaller objects like a model car would be measured in inches. Precise calculations are important as rough guesstimates might be way off the correct measurements.
Option b is correct.