Question

On a map, drawn to a scale of 1 : 250000, a triangular plot PQR of land has the following measurements : 

PQ = 3cm, QR = 4 cm and angles PQR = 90°

(i) the actual lengths of QR and PR in kilometer.
(ii) the actual area of the plot in sq . km.

Answer 1

Scale:-1 : 250000

∴1 cm represents 250000cm

`=(250000)/(1000xx100)=2.5 "km"`

 ∴ 1 cm  represent   2.5 km

Actual length of PQ = 3 × 2.5 = 7.5 km
Actual length of QR = 4 × 2.5 = 10 km

Actual length of PR=`sqrt((7.5)^2+(10)^2) "km" = 12.5 "km"`
(ii)
Area of ΔPQR =`1/2 xx PQ xx QR = 1/2(3)(4) "cm"^2=6 "cm"^2`
1 cm represents 2.5 km
1 cm² represents 2.5 × 2.5 km²
The area of plot = 2.5 × 2.5 × 6 km² = 37.5 km²