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 determine the height of the scale model, we need to use the given scale: 2 inches represents 30 feet. We can set up a proportion based on this scale to find the height of the model in inches.
Let represent the height of the scale model in inches.
Now, cross-multiply to solve for :
Now, divide both sides by 30:
Thus, the height of the scale model is 12 inches.
The correct answer is B. 12 inches.
Would you like more details or have any questions?
Here are 5 related questions you might find interesting:
- If the scale were changed to 1 inch representing 20 feet, what would be the new height of the scale model?
- How would the scale model change if the height of the stadium were 240 feet instead of 180 feet?
- What is the ratio of the height of the model to the actual stadium in simplest form?
- If the scale model's height were 24 inches, what would be the actual height of the stadium?
- How many inches would 90 feet of the actual stadium represent in the scale model?
Tip: Always make sure to keep units consistent when setting up proportions in scale problems!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Proportions
Scale Models
Formulas
\( \frac{2 \text{ inches}}{30 \text{ feet}} = \frac{x \text{ inches}}{180 \text{ feet}} \)
Theorems
Proportionality in scaling
Suitable Grade Level
Grades 6-8