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. 

Answer 1

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