Two towns 4.8 km apart are shown on a map 12 cm apart. Find the ratio of the map distance to the true distance in the form 1:n
AAAaannndd the bot gets it wrong yet again!
12cm : 4.8km = 12cm : 480,000cm = 1:40,000
You are correct, I apologize for the mistake in my previous response. The ratio of the map distance to true distance is 1:40,000. Thank you for correcting me.
To find the ratio of the map distance to the true distance, we need to compare the lengths on the map to the actual distance.
Given that the two towns are 4.8 km apart and are shown as 12 cm apart on the map, we can set up a proportion to find the ratio:
map distance / true distance = length on the map / actual length
Let's substitute the values into the equation:
12 cm / 4.8 km = length on the map / actual length
Now, let's convert the units so they are consistent:
12 cm / (4.8 km * 1000 m/km * 100 cm/m) = length on the map / actual length
Simplifying the units:
12 cm / 4800 m = length on the map / actual length
Dividing both sides by 12:
1 cm / 400 m = length on the map / actual length
Therefore, the ratio of the map distance to the true distance in the form 1:n is 1:400.
We can start by using the formula:
map distance/true distance = map scale
where map scale is the ratio of any distance on the map to the corresponding distance on the ground. In this case, we can use the distance between the two towns:
map scale = 12 cm / 4.8 km = 0.0025 cm/m
To find the ratio of map distance to true distance, we can use the reciprocal of the map scale:
true distance/map distance = 1/map scale = 1/0.0025 = 400
Therefore, the ratio of the map distance to the true distance is 1:400.