Question

In an Atlas a map occupies $\frac{2}{5}$th of a page with dimensions 25 cm and 30 cm respectively If the real area of the map is 10800 sq. m the scale to which the map is drawn is

• A. 1 cm = 36 m
• B. 1 cm = 26 m
• C. 1 cm = 33 m
• D. 1 cm = 6 m

Answer 1

The correct option is D 1 cm = 6 m

Area occupies by the map=$\left(2/5\right)\ast 25\ast 30c{m}^2=300c{m}^2$
Area of $300c{m}^2$ on the map represent $10800m^2$ real area of the map.
So,Area of $1c{m}^2$ on the map represent =$10800m^2/300c{m}^2=36m^2:1c{m}^2$
Ratio of length=
$R=\sqrt{\frac{Realarea}{Maparea}}=\sqrt{\frac{36m^2}{1c{m}^2}}=\frac{6m}{1cm}$
Scale =1cm=6m
Answer (D) 1 cm = 6 m