Math Is Fun Forum

LizzieD

Member

Registered: 2006-04-06

Posts: 3

simple ratio problem too much for me!

My son had this problem -
calculate the real area of a garden drawn in a plan, the scale is 1:2000.
The plan is a simple enough rectangle with two corners off the top so the calculation comes to
(3x5) cm2  - (1x1) cm2  = 15cm2 - 1cm2 = 14 cm2

We both thought then that the answer would be 14 cm2 x 2000 = 28000 cm2, but the area of the garden ended up being 5600m2:( where are we going wrong ?
Thanks for any explanations, sorry to be so dim!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: simple ratio problem too much for me!

2000 is the linear scale factor. When applied to areas, the scale factor is squared – in this case, 2000[sup]2[/sup] = 4000000. Hence

You can also calculate the actual area of the garden directly. The actual rectangle is 6000cm×10000cm, or 60m×100m. The square corner at the top is 2000cm×2000cm, i.e. 20m×20m. 60×100 − 20×20 = 5600.

Last edited by JaneFairfax (2007-06-28 02:21:09)

yvon.is

Member

Registered: 2009-01-21

Posts: 1

Re: simple ratio problem too much for me!

Is there a reference on here to explain scale ratios to someone who doesn't understand the first thing about it? How do you know when to put the number (ie: Height of roller coaster is 80m. Diagram height is 10 cm. What is the scale ratio?)

I am SO lost!! Is there a sure way method to know which number goes on the bottom (ie: 1/80 or the top, ie: 80/1)... I have no clue about this and I'm desperately trying to help my son, who is grade 8.

Please help!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: simple ratio problem too much for me!

10 cm on your model represents an actual length of 80 m. So your scale ratio is 10cm:80m, or 1cm:8m. 8 m = 800 cm. Hence your scale ratio is 1:800.