Math Problem Statement

Rishi is creating a scale drawing of his classroom inside this rectangle. His classroom is a 26-by-26-foot square. Which would create the best scale drawing of Rishi’s classroom for this rectangle?

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:

  1. How would you convert different dimensions using various scale factors?
  2. How can you calculate the total area represented by the scale drawing?
  3. What other objects might fit on this scale grid?
  4. How can you adjust scales if the classroom size changes?
  5. 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