You and your teammates have been hired to design a wall tapestry to be displayed in the arena foyer during the Conference on universal education. The tapestry is to be 12 feet wide by 36 feet high. Your initial sketch of the tapestry measured 8 inches by 24 inches. This initial sketch was a reduction by what percent (to the nearest) from the dimensions of the actual tapestry 

To calculate the percentage reduction from the dimensions of the actual tapestry to the dimensions of the sketch, we can use the formula for percentage reduction:

\[
\text{Percentage Reduction} = \left( \frac{\text{Actual Dimension} - \text{Sketch Dimension}}{\text{Actual Dimension}} \right) \times 100
\]

We'll calculate the percentage reduction for both the width and the height:

### Step 1: Convert feet to inches
Since the dimensions of the sketch are in inches, we'll convert the actual tapestry dimensions from feet to inches (1 foot = 12 inches):

- Actual width: \(12 \text{ feet} \times 12 \text{ inches/foot} = 144 \text{ inches}\)
- Actual height: \(36 \text{ feet} \times 12 \text{ inches/foot} = 432 \text{ inches}\)

### Step 2: Calculate percentage reduction for width
The width of the sketch is 8 inches, and the actual width is 144 inches. Applying the formula:

\[
\text{Percentage Reduction (width)} = \left( \frac{144 - 8}{144} \right) \times 100 = \left( \frac{136}{144} \right) \times 100 \approx 94.44\%
\]

### Step 3: Calculate percentage reduction for height
The height of the sketch is 24 inches, and the actual height is 432 inches. Applying the formula:

\[
\text{Percentage Reduction (height)} = \left( \frac{432 - 24}{432} \right) \times 100 = \left( \frac{408}{432} \right) \times 100 \approx 94.44\%
\]

### Final Result
The reduction from the actual dimensions to the sketch is approximately **94.44%** for both the width and the height.

Would you like more details or have any questions?

Here are some related questions:
1. How would the sketch dimensions change if the tapestry were 50 feet tall instead?
2. What are the ratios of the sketch to the actual tapestry for both dimensions?
3. How can you scale the sketch if the tapestry's height changes but the width remains the same?
4. If the tapestry was designed in a different shape, how would this impact scaling?
5. What other factors should be considered when designing large-scale images for public display?

**Tip:** Always ensure units are consistent when comparing or scaling measurements.

You and your teammates have been hired to design a wall tapestry to be displayed in the arena foyer during the Conference on universal education. The tapestry is to be 12 feet wide by 36 feet high. Your initial sketch of the tapestry measured 8 inches by 24 inches. This initial sketch was a reduction by what percent (to the nearest) from the dimensions of the actual tapestry?

Learn how to calculate the percentage reduction from a sketch of a tapestry to the actual size for a project. The problem covers percentage reduction and unit conversion, applying them to real-world scenarios involving measurements in feet and inches. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation