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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.
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Solution
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
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