Question

A rectangular area of 12 km² is represented by 1.5 cm × 0.5 cm rectangle on a map. The scale of the map is:
1. 1 : 400000
2. 1 : 12000
3. 1 : 16000
4. 1 : 1000

Answer 1

Correct Answer - Option 1 : 1 : 400000

Concept:

The various type of scales in photography are:

a) Linear or length scale \(= \frac{{length\;of\;on\;object\;on\;Map}}{{length\;of\;same\;object\;on\;ground}}\)

b) Area scale \(= \frac{{Area\;of\;on\;object\;on\;Map}}{{Area\;of\;an\;object\;on\;ground}}\)

Calculation:

Here object is a “rectangle”

Area of rectangle on MAP = 1.5 × .5 = 0.75 cm²

Area of rectangle on ground = 12 km² (given)

Area scale \( = \frac{{\left( {0.75\; \times \;{{10}^{ - 4}}} \right){m^2}}}{{\left( {12\; \times \;{{10}^6}} \right){m^2}}} = \left( {\frac{1}{{16\; \times \;{{10}^{10}}}}} \right)\)

This is not given, so we calculate, length scale

(length scale) = (width scale)

\(\frac{L}{{1.5}} = \frac{B}{{0.5}}\)   [L, B are length and breadth of rectangle an ground]

⇒ L = 3D

Further given that L × B = 12

3B × B = 12 ⇒ B = 2 km and L = 6 km

Now, linear length scale \( = \left( {\frac{{1.5\; \times\; {{10}^{ - 2}}}}{{6\; \times\; {{10}^3}}}} \right) = \frac{1}{{40,0000}}\)