Math Problem Statement

An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet.

What is the height of the scale model in inches? A.3 in. B.12 in. C.60 in. D.105 in.

Solution

To solve this problem, we can use a proportion based on the given scale:

  • 2 inches in the model represents 30 feet in real life.
  • The height of the actual stadium is 180 feet.

We can set up a proportion to find the height of the model, denoted by xx (in inches):

2 inches30 feet=x inches180 feet\frac{2 \text{ inches}}{30 \text{ feet}} = \frac{x \text{ inches}}{180 \text{ feet}}

Now, solve for xx:

x=2×18030=36030=12 inchesx = \frac{2 \times 180}{30} = \frac{360}{30} = 12 \text{ inches}

Thus, the height of the scale model is 12 inches, so the correct answer is:

B. 12 in.

Would you like further details on proportions or scaling? Here are some related questions:

  1. What is the length of a real object if it is 8 inches in the model using the same scale?
  2. How would the scale model's height change if the scale were 1 inch = 15 feet?
  3. How do you calculate the scale factor between two different scales?
  4. What is the model height if the actual stadium height is doubled?
  5. How can this concept be applied to creating blueprints or maps?

Tip: When dealing with scales, always make sure units are consistent before setting up proportions.

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Math Problem Analysis

Mathematical Concepts

Ratios
Proportions
Scaling

Formulas

(Model Height / Real Height) = (Scale Model Length / Real Length)

Theorems

Proportionality Theorem

Suitable Grade Level

Grades 6-8