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Question
On a map drawn to a scale of 1 : 25000, a triangular plot of a land is marked as ABC with AB= 6cm, BC = 8cm and ∠ ABC = 90° . Calculate the actual length of AB in km and the actual area of the plot in km2 .
Solution
Scale : - : 1 : 25000
∴ 1 cm represents 25000 cm = `25000/(1000 xx 100) = 2.5` km
∴ 1 cm represents 0.25 km
Actual length of AB = 6 × 0.25 = 1.50 km
Area of Δ ABC = `1/2 xx "BC" xx "AB"`
`= 1/2 xx 8 xx 6 = 24 "cm"^2`
1 cm represents 0.25 km
1 cm2 represents 0.25 × 0.25 km2
The area of plot = 0.25 × 0.25 × 25 km2
= .0625 × 24
= 1.5 km2
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