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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:
- the actual lengths of AB and BC in km.
- the area of the plot in sq. km.
Solution
Scale of map drawn of a triangular plot
= 1 : 2,50,000
∴ k = 250000
Measurement of plot
AB = 3 cm, BC = 4 cm and ∠ABC = 90°
i. Actual length of AB = 3 × 250000 cm
= `(3 xx 250000)/100 m`
= `(3 xx 250000)/(100 xx 1000) km`
= `15/2`
= 7.5 km
And actual length of BC
= `(4 xx 250000)/(100 xx 1000)`
= 10 km
ii. Area of plot
= `1/2 xx BC xx AB`
= `1/2 xx 7.5 xx 10 km^2`
= `75/2`
= 37.5 km2
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