Verified answer

Step-by-step explanation:

Complete step by step solution:

We are given that the scale of the map is 1:4000000 . This means that 1 unit in the graph is equivalent to 4000000 units in actual.

We need to find the actual distance between two cities which is 5cm apart in the map.

Let x be the actual distance between the two cities. So, we can write it as a ratio of distance on the map to the actual distance

⇒5:x

This ratio will be proportional to the given scale of the map. So, we can write them as,

⇒14000000=5x

On cross multiplying, we get

⇒x=5×4,000,000

On simplification, we get

⇒x=20,000,000

As the distance on the map is 5 cm, the unit of x will be in cm.

⇒x=20,000,000cm

We know that 1cm=1100m . So, x will become

⇒x=20,000,000100m

We also know that 1m=11000km . So, x will become

⇒x=20,000,000100×1000km

On cancelling the zeros, we get,

⇒x=200km

Therefore, the actual distance between two cities is 200 km.

ALTERNATE SOLUTION :-

We are given that the scale of the map is 1:4000000 . This means that 1 unit in the graph is equivalent to 4000000 units in actual.

So 5cm in the map will be equal to 5 times 4000000 cm.

⇒d=5×4,000,000cm

We can write the zeros as powers of 10.

⇒d=5×4×106cm

On multiplication, we get

⇒d=20×106cm

We know that 1cm=10−2m and 1m=10−3km . So, 1cm=10−5km

So, the distance will become,

⇒d=20×106×10−5km

On cancelling the powers, we get,

⇒d=20×10km

On simplification we get,

⇒d=200km

Therefore, the actual distance between two cities is 200 km.