Math Problem Statement
Solution
Rishi's classroom is a 26-by-26-foot square, and he wants to create a scale drawing inside a rectangle. Based on the image, the grid is 10 units by 10 units.
To create the best scale drawing, we need to select a scale that fits the 26-by-26-foot classroom inside the 10-by-10-unit grid without distortion.
Here’s how the options work:
- 1 unit to 2 feet: A 10-unit by 10-unit grid would represent a 20-foot by 20-foot classroom (10 units × 2 feet = 20 feet). This is too small for Rishi's 26-foot classroom.
- 1 unit to 3 feet: A 10-unit by 10-unit grid would represent a 30-foot by 30-foot classroom (10 units × 3 feet = 30 feet). This would fit the 26-foot classroom well, with a bit of extra space.
- 1 unit to 10 feet: A 10-unit by 10-unit grid would represent a 100-foot by 100-foot space, which is too large for the 26-foot classroom.
- 3 units to 1 foot: This would be a very compressed scale, where a 26-foot classroom would require 78 units (26 feet × 3 units). Since the grid only has 10 units per side, this would not work.
Thus, 1 unit to 3 feet is the best scale for the drawing because it allows Rishi’s classroom to fit comfortably within the grid.
Would you like more details on how I approached this, or do you have any questions?
Here are five related questions:
- How would you convert different dimensions using various scale factors?
- How can you calculate the total area represented by the scale drawing?
- What other objects might fit on this scale grid?
- How can you adjust scales if the classroom size changes?
- What are the advantages of different scale units in drawings?
Tip: Always check both the length and width when choosing a scale to ensure both dimensions fit.
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Math Problem Analysis
Mathematical Concepts
Scale Factor
Geometry
Measurement Conversion
Formulas
Scale factor formula: Drawing Dimension = Actual Dimension × Scale
Theorems
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Suitable Grade Level
Grades 5-7