Question

On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:

1) the actual length of the diagonal distance AC of the plot in km.

2) the actual area of the plot in sq. km.

Answer 1

Scale: 1:50000

1 cm represents 50000 cm = `50000/(1000xx100)` =   0.5km

1) In ΔABC, by pythagoras theorem

AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100

⇒ AC = 10 cm

⇒ Actual length of diagonal AC = 10 x 0.5 = 5 km

2) 1 cm = 0.5 km

`=> 1 cm^2 = 0.25 km`

Area of rectangle ABCD = AB x BC = 6 x8 = 48 cm²

⇒ Actual area of a plot = 48 x 0.25 = 12 km²