1. Determine the usable page dimensions:
   • Page size: 12 by 12 inches.
   • Margins: 0.75 inches on all sides.
   • Usable dimensions: \(12 - 2 \times 0.75 = 10.5\) inches.
2. Identify the longest dimension of India:
   • North to south: 3,214 kilometers.
   • West to east: 2,933 kilometers.
   • Longest dimension: 3,214 kilometers.
3. Set up the scale equation:
   • The longest dimension of India (3,214 km) should fit exactly in the usable page height (10.5 inches).
   • Scale \(k\) (kilometers per inch): \(k = \frac { 3214} { 10.5} \).
     Thus, the equation is \(k = \frac { 3214} { 10.5} \).

Supplemental Knowledge

Cartographers who create maps must often reduce large geographical areas so as to fit onto manageable pages, using scale factors - the ratio between actual distance and map distance that ensure all dimensions are proportionally reduced or expanded - when creating their maps. This involves using scale factors.
Under 1:100,000 scale maps, one unit on the map corresponds to 100,000 real units in real life. Uche must determine an adequate scale so that India fits within his usable space on his atlas page.

Concepts to Actions

Imagine you are designing the blueprints for a new building. By selecting an appropriate scale and drawing sheet size, it should be easy for you to ensure every room and hallway in your plan are accurately represented on paper while staying within its boundaries. With accurate plans in hand, construction workers should follow along according to your design!

Understanding concepts like scaling and proportions is crucial for various fields such as cartography, architecture, and engineering. At UpStudy, we provide resources that help you master these essential skills through interactive lessons and expert guidance. For detailed insights into geometry and measurement or other mathematical topics, explore UpStudy’s live tutor question bank or our AI-powered problem-solving services.
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