Ask a New Question
Menu

A student made a model of the Eiffel Tower using a scale in which 1 inch represents 12 feet. The actual Eiffel Tower is 984 feet tall.

3 answers

To determine the height of the model of the Eiffel Tower in inches, you can use the scale provided: 1 inch represents 12 feet.

First, start with the actual height of the Eiffel Tower:

  1. Actual height = 984 feet
  2. Scale conversion: 1 inch = 12 feet

Now, to convert the actual height into model height (in inches), you can use the formula:

\[ \text{Model height (in inches)} = \frac{\text{Actual height (in feet)}}{\text{Scale (in feet per inch)}} \]

Substituting the values:

\[ \text{Model height (in inches)} = \frac{984 \text{ feet}}{12 \text{ feet per inch}} = 82 \text{ inches} \]

Therefore, the height of the model of the Eiffel Tower is 82 inches.

How did you solve

To solve for the height of the model of the Eiffel Tower in inches, I followed these steps:

  1. Identify the Actual Height: The actual height of the Eiffel Tower is given as 984 feet.

  2. Understand the Scale: The scale provided states that 1 inch represents 12 feet.

  3. Set Up the Conversion Equation: To find the height of the model in inches, I needed to convert the actual height in feet to the model height in inches using the scale. The conversion can be expressed using the formula: \[ \text{Model height (in inches)} = \frac{\text{Actual height (in feet)}}{\text{Scale (in feet per inch)}} \]

    In this case:

    • The actual height is 984 feet.
    • The scale tells us that for every 1 inch on the model, it represents 12 feet in reality.

  4. Perform the Calculation: Substituting the known values into the formula: \[ \text{Model height (in inches)} = \frac{984 \text{ feet}}{12 \text{ feet per inch}} \]

    Calculating this gives: \[ \text{Model height (in inches)} = 82 \text{ inches} \]

  5. Conclusion: The height of the model of the Eiffel Tower, based on the provided scale, is 82 inches.

This straightforward approach allowed me to convert the actual height of the structure into the model height by using simple division corresponding to the scale factor.