Why the answer is 1:500 but not 1:250000

Question

The actual area of a playground is 900m².If the area of the playground on a map is 36 cm²,then the scale of the map is?

i thought the answer is 36:900*100*100=1:250000 but is wrong

Answer 1

To put that in simpler terms, the scale goes by the lengths of the sides. If the playground is 45 m x 20 m, that's 450 cm x 200 cm, and the map is 9 x 4 cm, so your ratio is 45:9 or 200:4 = 50:1.

Answer 2

Your problem is that the scale is a linear measure and your have been given area measures which are proportional to the square of the linear scale.

 

Therefore, the scale is the square root of the area ratio i.e. the square root of 900/36 = 30 m/6 cm = 3000/6 = 500/1.

 

I hope that helps!

Answer 3

The linear scale factor must be squared to represent the comparative areas.

 

Working backwards, in this case, you take the square root of ratio of area.

 

900 sq m/36 sq cm = 25 sq m / 1 sq cm = 250000 sq cm/1 sq cm.

 

1:250000 when square root is taken to get the linear relationship becomes 1:500.