Geometry

[Studyinghard]

A 1:10000 map shows a lake. The area of the lake on the map is 1.2cm^2. the area of the real lake is sq. km is?

[mojomojo]

1.2 times 100000000 then divide it by 1000000? which equals 120km^2.

because...

10000 = length so 10000^2 = area.

1.2cm^2 on map then equals 120000000cm^2 of real lake...then converts it back to km^2..=120km^2?

please tell me the answer.

[Studyinghard]

nope

[captain_kirk]

well assuming the ratio of 1:10000 is in cm
you'd straight off the bat convert it to km
so it'd be 1/1000:10000/1000
which is .001:10
so the ratio of lengths are easy enough

then you'd take the the 1.2cm^2 back to cm, by square rooting it
so it'd be 1.09545cm, which you'd convert straight to km as well, so it'd be 0.001095
then you have the ratios for both, its simple
.001/10=0.001095/x
x=(10 x 0.001095)/.001
x = 10.9545

then to get area you'd just square it
so area = 10.9545^2 = 120km^2

[linahh123]

get the ratio of the area : 1:100000000

then 1.2 x 100000000

then divide answer by (100x100x1000x1000)   to convert to km^2

answer is 0.012km^2?

[mojomojo]

well assuming the ratio of 1:10000 is in cm
you'd straight off the bat convert it to km
so it'd be 1/1000:10000/1000
which is .001:10
so the ratio of lengths are easy enough

then you'd take the the 1.2cm^2 back to cm, by square rooting it
so it'd be 1.09545cm, which you'd convert straight to km as well, so it'd be 0.001095
then you have the ratios for both, its simple
.001/10=0.001095/x
x=(10 x 0.001095)/.001
x = 10.9545

then to get area you'd just square it
so area = 10.9545^2 = 120km^2

That's what i said and he said nope. D:

[Studyinghard]

get the ratio of the area : 1:100000000

then 1.2 x 100000000

then divide answer by (100x100x1000x1000)   to convert to km^2

answer is 0.012km^2?

thats it, thanks

[linahh123]

Do you understand my steps?

[linahh123]

well assuming the ratio of 1:10000 is in cm
you'd straight off the bat convert it to km
so it'd be 1/1000:10000/1000
which is .001:10
so the ratio of lengths are easy enough

then you'd take the the 1.2cm^2 back to cm, by square rooting it
so it'd be 1.09545cm, which you'd convert straight to km as well, so it'd be 0.001095
then you have the ratios for both, its simple
.001/10=0.001095/x
x=(10 x 0.001095)/.001
x = 10.9545

then to get area you'd just square it
so area = 10.9545^2 = 120km^2

That's what i said and he said nope. D:

You used the ratio of the length instead of the ratio of the area

[mojomojo]

Oo, thanks linahh123.

I failed to convert it back to km^2.