Question

On a map drawn to a scale of 1:2,50,000; a triangular plot of land has the following measurments : AB= 3 cm, BC= 4 cm and $\angle ABC={90}^{\circ }$.

Calculate the actual lengths of AB and BC in km. Then the area of the plot in sq. km. is

• A. $26.5k{m}^2$
• B. $32.5k{m}^2$
• C. $37.5k{m}^2$
• D. $42.5k{m}^2$

Answer 1

The correct option is C

$37.5k{m}^2$

Scale of map drawn of a triangular plot = 1: 2,50,000

Measurements of the plot:

AB= 3 cm, BC= 4 cm and $\angle ABC={90}^{\circ }$



Actual length of AB $=3\times 250000cm$

$=\frac{3\times 250000}{100}m$

$=\frac{3\times 250000}{100\times 1000}$

$=\frac{15}{2}=7.5km$

Actual length of BC$=\frac{4\times 250000}{100\times 1000}=10km$

Now, the area of plot $=\frac{1}{2}\times BC\times AB$

$=\frac{1}{2}\times 7.5\times 10k{m}^2$

$=\frac{75}{2}=37.5k{m}^2$