Question

On a map drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = 90°.

Calculate:

1. the actual lengths of AB and BC in km.
2. the area of the plot in sq. km.

Answer 1

Scale of map drawn of a triangular plot

= 1 : 2,50,000

∴ k = 250000

Measurement of plot

AB = 3 cm, BC = 4 cm and ∠ABC = 90°

i. Actual length of AB = 3 × 250000 cm

= `(3 xx 250000)/100 m`

= `(3 xx 250000)/(100 xx 1000) km`

= `15/2`

= 7.5 km

And actual length of BC

= `(4 xx 250000)/(100 xx 1000)`

= 10 km

ii. Area of plot

= `1/2 xx BC xx AB`

= `1/2 xx 7.5 xx 10  km^2`

= `75/2`

= 37.5 km²