On a map, drawn to a scale of 1 : 20000, a rectangular plot of land ABCD has AB = 24cm and BC = 32 cm. Calculate:
(i) the diagonal distance of the plot in kilometer
(ii) the area of the plot in sq.km
Scale :- 1 : 20000
(i)
AC2 = AB2 + BC2
= 242 + 322
= 576 + 1024 = 1600
AC = 40 cm
Actual length of diagonal = 40 × 0.2 km = 8 km
(ii)
1 cm represents 0.2 km
1 cm2 represents 0.2 × 0.2 km2
The area of the rectangle ABCD = AB × BC
= 24 × 32 = 768 cm2
Actual area of the plot = 0.2 × 0.2 × 768 km2 = 30.72 km2
