Question

Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 121212 by 121212 inches, with 0.750.750, point, 75 inch margins on all 444 sides. India measures 3{,}2143,2143, comma, 214 kilometers from north to south and 2{,}9332,9332, comma, 933 kilometers from west to east. Uche wants the longest dimension of India to fit exactly in between the margins of the page. If kkk is the number of kilometers per inch in Uche's scale, which equation best models the situation

Answer 1

The scale ratio of a point A to another point B is the division of the length of B by the length of A. The best equation that models the situation is: $10.5k= 3214$

The page dimension is:

$Length = 12$

$Width = 12$

The length and the width of Uche's book are equal; this means the pages of Uche's book have the shape of a square

The margin of 0.75 on either sided means the usable dimension is:

$Length = 12 - 2 * 0.75 =10.5$

The dimension of India is:

$Length = 3214$

$Width =2933$

The longest side in India's dimension is:

$Longest = 3214$

From Uche's book, the longest dimension is:

$Longest = 10.5$

So, the scale equation is:

k * longest length of Uche's book = longest side of India

This gives:

$k * 10.5 =3214$

$10.5k =3214$

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