Mathematics
On a map drawn to a scale of 1 : 20000, a rectangular plot of land ABCD has AB = 32 cm and BC = 24 cm. Calculate :
(i) the diagonal distance of the plot in km,
(ii) the area of the plot in sq. km.
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Answer
(i) By pythagoras theorem,
⇒ AC2 = AB2 + BC2
⇒ AC2 = 322 + 242
⇒ AC2 = 1024 + 576
⇒ AC2 = 1600
⇒ AC = = 40 cm.
Given,
Scale of map =
Length of diagonal distance in map = k × Actual length of diagonal of plot
40 = × Actual length of diagonal of plot
Actual length of diagonal of plot = 40 × 20000 = 800000 cm
= = 8 km.
Hence, diagonal distance of plot = 8 km.
(ii) Area of plot on map = AB × BC = 24 × 32 = 768 cm2
Area of plot on map = k2 × Area of actual plot
768 = × Area of actual plot
Area of actual plot = 768 × 20000 × 20000 cm2
= km2
= 30.72 km2
Hence, area of plot = 30.72 km2.
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