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Maxwell Elliott

07/13/2024 · Primary School

Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 12 by 12 inches, with 0.75 inch margins on all 4 sides. India measures 3,214 kilometers from north to south and 2,933 kilometers from west to east. Uche wants the longest dimension of India to ft exactly in between the margins of the page. If k is the number of kilometers per inch in Uche's scale, which equation best models the situation?

Answer
expertExpert-Verified Answer

Ayala Young
Specialized Tutor
4.0 (47votes)

\(k = \frac { 3214} { 10.5} \)

 

Solution

  1. The page size is 12 by 12 inches, with 0.75-inch margins on all four sides.
  2. Subtract the margins from the page size to get the usable area: \(12 - 2 \times 0.75 = 10.5\) inches.
  3. The longest dimension of India is 3,214 kilometers (north to south).
  4. To fit this dimension exactly within the usable area, set up the equation where the longest dimension of India (3,214 km) equals 10.5 inches on the map.
  5. The scale \(k\) (kilometers per inch) is \(\frac { 3214 \text { km} } { 10.5 \text { inches} } \).

 

Supplemental Knowledge

As with creating any scale model, such as a map, creating one requires mastering how to transform real world dimensions into manageable sizes while keeping proportions intact. This involves using ratios correctly across units of measurement.

 

Theory in Practice

Consider what it would be like if you were trying to design a garden: fitting different plants within an area without overcrowding. By making accurate scale drawings of every aspect of the area where plants will go, you can accurately plan their placement, giving each the room to grow as intended. Uche applies this same principle when fitting India onto one atlas page.

 

To master concepts like scaling and proportions, explore UpStudy’s live tutor question bank or our AI-powered problem-solving services. Our resources provide detailed explanations and interactive learning experiences tailored to your needs.
For those looking to enhance their mathematical skills further, UpStudy offers comprehensive guides that make learning both engaging and effective!

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