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A model of a treehouse is made using a scale of 1 inch: 3 feet. What is the height of the actual treehouse if the height of the model is 5 1/3 inches?

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Final answer:

The height of the actual treehouse is 16 feet, calculated by multiplying 5 1/3 inches (converted to an improper fraction) by the scale of 1 inch equaling 3 feet.

Step-by-step explanation:

The question asks us to determine the actual height of a treehouse given the height of its scale model and the scale ratio. The scale given is 1 inch equals 3 feet, and the model's height is 5 1/3 inches. To find the height of the actual treehouse, we will convert 5 1/3 inches to an improper fraction, which is 16/3 inches, and then multiply by the scale factor. Since 1 inch corresponds to 3 feet on the actual treehouse, we have:

  1. First, convert 5 1/3 inches to an improper fraction: 5 1/3 = (5 × 3 + 1)/3 = 16/3 inches.
  2. Second, multiply the model's height by the scale factor: (16/3) × 3 feet/inch = 16 feet.

Therefore, the actual height of the treehouse is 16 feet.

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