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, ∠ABC = 90°.

Calculate:

1. The actual length of AB in km.
2. The area of the plot in sq. km.

Answer 1

Scale = 1 : 25000

(i)

Actual length of AB = 3 × 250000 cm

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

= 7.5 km

∴ AB = 7.5 km

(ii)

Actual length of BC = 4 × 250000 cm

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

= 10 km

∴ BC = 10 km

Area(ΔABC) = `(1)/(2) xx "AB" xx "BC"`

Area(ΔABC) = `(1)/(2) xx 7.5 xx 10" km"^2`

Area(ΔABC) = 37.5 km²

Area of plot = 37.5 km²