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Question
On a map drawn to a scale of 1 : 25000, a rectangular plot of land, ABCD is measured as AB= 12 cm and BC = 16cm. calculate the diagonal distance of the plot in km and the plot area in km2 .
Solution
Scale :- 1 : 25000
1 cm represents 25000 cm = `25000/(1000 xx 100) = 0.25` km
1 cm represents 0.25 km
AC2 = AB2 + BC2
= 122 + 162
= 144 + 256
AC2 = 400
AC = 20 cm
Actual length of diagonal = 20 × 0.25 = 5.00 = 5 km
1 cm represents 0.25 km
1 cm2 represents 0.25 × 0.25 km2
The area of the rectanggle ABCD = AB × BC
= 16 × 12 = 192 cm2
The area of the plot = 0.25 × 0.25 × 192 km2 = 12 km2
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