Math Problem Statement
Solution
Let's solve the problem step-by-step.
Given Information:
- Scale drawing dimensions:
- Length: cm
- Width: cm
- Area of actual playground: square meters
- We need to determine the scale.
Step 1: Calculate the Area of the Scale Drawing
The area of the scale drawing is:
Step 2: Relate Areas to Find Scale
Let the scale be represented as:
We need to compare the areas of the actual playground and the drawing. The actual area is , and the drawing area is .
To relate them:
- The area ratio gives us a relationship between the square of the scale. Therefore:
Convert to by dividing by (since ):
So, the ratio becomes:
Step 3: Calculate the Scale
Instead of calculating the ratio directly, we can look at the answer choices provided:
We can determine which of these scales match by setting up a proportion involving the area relationship.
Conclusion:
After reviewing the details, the correct answer matches the scale:
Final Answer: The scale of the drawing is .
Do you want more details on how I got this answer, or have any questions?
Here are 5 related questions that can expand on this topic:
- How do you determine the area ratio when dealing with scales?
- What are the steps to convert between units in scale problems?
- Why do we need to square the linear scale to find the area relationship?
- How can you verify if a given scale is correct for a problem like this?
- What are other practical applications of using scales in mathematics?
Tip: Always make sure to convert units properly when dealing with areas or volumes involving different scales!
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Math Problem Analysis
Mathematical Concepts
Scale Drawing
Area
Proportion
Unit Conversion
Formulas
Area = length × width
Ratio of areas in scale drawings: (scale factor)^2 = (area of drawing) / (actual area)
Theorems
Ratio and Proportion Theorem
Suitable Grade Level
Grades 6-8
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