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Question

On a map, drawn to a scale of 1 : 2,50,000; a triangular plot of land has the following measurements : AB = 3 cm, BC = 4 cm and angle ABC = 90. Calculate : (i) the actual lengths of AB and BC in km. (ii) the area of the plot in sq. km.

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Solution

Scale:-1 : 250000

∴ 1 cm represents 250000cm

= 2500001000×100

= 2.5

(i)

Actual length of AB = 3×2.5 = 7.5 km

Actual length of BC = 4×2.5 = 10 km

The actual length of AC = 7.52+102 = 12.5 Km

2nd-

Area of ABC = 12AB×BC

= 12×3×4 = 6cm2


1cm represents 2.5 Km
1cm2 represents 2.5×2.5km2
The area of plot = 2.5×2.5×6 = 37.5 km2


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