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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 ∠ABC = 90°.
Calculate : the actual lengths of AB and BC in km.
Solution
The ratio of the length of two corresponding sides of two similar triangles.
The scale factor is 1 : 2,50,000.
The length of AB on the map = `1/(2,50,000)` (the actual length of AB)
`=> 3 = 1/(2,50,000)` (the actual length of AB)
`=>` the actual length of AB = 3 x 2,50,000
`=>` the actual length of AB = 7,50,000 = 7.5 km
The length of BC on the map = `1/(2,50,000)` (the actual length of BC)
`=> 4 = 1/(2,50,000)` (the actual length of BC)
`=>` the actual length of BC = 4 x 2,50,000
`=>` the actual length of BC = 1,00,000 = 10 km
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