Question

A model of a sailing boat is made to the scale
1 : 50, i.e a length of 1 cm on the model
represents 50 centimetres on the real yacht.
If one of the sails on the real yacht has an area
of 5 m² what will be the area of the same sail
on the model?

Answer 1

Answer:

$20cm^2$

Step-by-step explanation:

We are talking of a linear scale ie 1 cm = 50 cm

So if the real yacht length is 10 meters(10,000 cm), then the model length will be 10000/50 = 200 cm

However, when talking about areas, the scale factor is different. We cannot simply divide 5m by 50

Let's say the sail height is 1 meter and the sail width is 5 meters which will give a sail area of 5 sqm.

The scaled height would be 100/50 = 2cm and scaled width will be 500/50 = 10 cm

So the area of the sail on the model will be 2 x 10 =200 square cm

In short, area of sail on model = (area of sail on real yacht( ÷ (50 x 50)

Since there are 10,000 square cm to 1 square meter we get the answer as 5 x 10000/2500 = 20 square cm