Question 720122: how to solve this question ?
1) a road is 2 km long. what is the length of the road on a map of scale 1:20000 ?
2) a map uses a scale of 1:5000. what is the actual length of a river if it measures 5cm on the map? give your answer in km. .
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the attached reference give some insight into the scale on a map.
http://egsc.usgs.gov/isb/pubs/factsheets/fs01502.pdf
assuming they are talking about inches, then the scale can be interpreted as follows:
1 inch on the map represents 20,000 inches in the real world.
1 km in the real world is equivalent to 39,370.1 inches.
2 km in the real world would be equivalent to 2 * 39,370.1 which would be equal to 78,740.2 inches.
2 km in the real world is equivalent to 78740.2 inches.
the ratio to the map is:
1 / 20,000 = x / 78,740.2
solve for x and you get x = 78,740.2 / 20,000 = 3.93701 inches.
3.93701 inches on the map represents 2 kilometers in the real world.
assuming they are talking about centimeters, then the ratio of 1:20,000 would be analyzed as follows:
1 km in the real world is equivalent to 100,000 centimeters.
2 km in the real world is therefore equivalent to 200,000 centimeters.
with a scale 1 centimeter on the map to 20,000 centimeters in the real world, the equivalent measure on the map would be:
200,000 / 20,000 = 10 centimeters on the map.
we assumed inches and we got 3.93701 inches on the map is equivalent to 2 kilometers in the real world.
we assumed centimeters and we got 10 centimeters on the map is equivalent to 2 kilometers in the real world.
since an inch is equivalent to 2.54 centimeters, we can convert the measurement on the map from centimeters to inches by dividing by 2.54.
when we do that, 10 centimeters on the map is equivalent to 3.93701 inches on the map.
in other words, we got the same measure on the map whether or not we assumed inches or centimeters.
3.93701 inches is equivalent to 10 centimeters.
if we assumed inches, we would measure 3.93701 inches.
if we assumed centimeters, we would measure 10 centimeters.
the actual distance on the map would be the same.
to answer the second question you posed, centimeters on the map is assumed.
5 centimeters on the map is equivalent to how many kilometers in the real world.
the scale of the map is 1:5,000
this means that 1 cm on the map is equivalent to 5,000 cm in the real world.
if the distance on the map is 5 cm, then the distance in the real world is 5 * 5,000 cm which is equal to 25,000 cm.
since 1 km is equivalent to 100,000 cm in the real world, then 25,000 cm is equivalent to 25,000 / 100,000 = .25 kilometers.
Answer by ikleyn(53332)  (Show Source):
You can put this solution on YOUR website! .
how to solve this question ?
1) a road is 2 km long. what is the length of the road on a map of scale 1:20000 ?
2) a map uses a scale of 1:5000. what is the actual length of a river if it measures 5cm on the map?
give your answer in km.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
(1) A road is 2 kilometers long. 2 kilometers is 2000 meters.
The scale 1 : 20000 means that 1 centimeter on the map is 20000 centimeters in the field.
It is the same as to say that 1 centimeter on the map is 200 meters in the field.
2000 meters is 10 times 200 meters.
Hence, according to common sense (or the law of proportion), 10 centimeters on the map is 2000 meters in the field.
Thus the length of the road on the map is 10 centimeters. <<<---=== ANSWER.
(2) A map uses a scale of 1:5000. It means that 1 cm on the map corresponds to 5000 cm in the field,
i.e. 1 cm on the map corresponds to 50 meters in the field.
Hence, according to common sense (or the law of proportion),
5 centimeters on the map corresponds to 5*50 = 250 meters in the field. <<<---=== ANSWER
That's all. It sounds as a song or as a poem. Because the common sense follows to law of harmony.
Now compare it with the composition by @Theo in his post.
It is a collapse of a brain. Why inches ? Why these unnecessary conversions ? Nobody asked about inches . . .
Nobody asked about these decimal fractions . . . It is a collapse . . .
I advise you to ignore the post by @Theo - escape and run from it - - - as fast and as far as you can.
I completed.
My reader, I wish you to live in harmony forever, with a well-functioning brain.
In such simple problems/assignments, you better lean on your common sense rather than crazy compositions.
When you learn Math (or Science, or everything),
it is of critically importance to learn from good sources.
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