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:
(i) The actual length of AB in km.
(ii) The area of Plot in sq. km.

Answer 1

Scale = 1: 25000
(i) Actual length of AB
= 3 x 250000cm

= `(3 xx 250000)/(100 xx 100)`km
= 7.5km
AB = 7.5km.

(ii) Actual length of BC
= 4 x 250000cm

= `(4 xx 250000)/(100 xx 100)`km
= 10km
BC = 10km

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

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

Area(ΔABC) = 37.5km²
Area of plot = 37.5km².