Let's go through each question based on the information given.

Question 1

You can also write an equation for equivalent ratios. The equation at the right can be used to find the actual length $x$ of the sculpture room in the museum. Complete the equation and explain what each part represents.

Assuming that the scale is given as $1$ centimeter represents a certain number of meters (as shown by "1 centimeter = ... x meters"), you would set up the equation as follows:

1. Let $1$ centimeter represent $x$ meters in real life.
2. The equation could look something like: $\frac{1 \, \text{cm}}{x \, \text{meters}} = \frac{\text{model length in cm}}{\text{actual length in meters}}$

Each part of this equation:

• 1 cm: Represents 1 unit of length on the scale drawing (or model).
• x meters: Represents the actual length in the museum that corresponds to 1 cm on the model.
• Model length in cm / Actual length in meters: Shows how the scale can be applied to find the real measurements from the model.

Question 2

How can you use the equation to find the actual length of the sculpture room?

To find the actual length of the sculpture room, you would:

1. Measure the length of the sculpture room on the model in centimeters.
2. Use the equivalent ratio (or scale) to set up a proportion with the known scale (from the equation in Question 1).
3. Solve for the actual length by cross-multiplying and isolating the variable if necessary.

Question 3

Write and solve an equation to find the actual width of the sculpture room.

1. Measure the width of the sculpture room on the model.
2. Set up the proportion: $\frac{1 \, \text{cm}}{x \, \text{meters}} = \frac{\text{model width in cm}}{\text{actual width in meters}}$
3. Solve for the actual width by cross-multiplying and solving for the width in meters.

Let me know if you need more detailed explanations on setting up or solving these equations, or if you’d like further clarification.

Here are five related questions to deepen your understanding:

1. What are some other examples of scale drawings you encounter in daily life?
2. How would you determine the scale if only the model measurements and actual measurements are known?
3. How does changing the scale factor affect the actual size represented in the model?
4. Why is understanding scale important in fields like architecture or engineering?
5. How could you verify that your calculations for actual length or width are correct?

Tip: Always check that units are consistent when working with scale ratios to avoid calculation errors.