When we present large objects or distance using photographs or maps, we are using reduction to scale down. If we want to find the length of the real-world object from the photograph or map, we need to know the proportional ratio between the image and the real object which is called the scale ratio. If a image has a scale ratio attached to it, we can call it a scale drawing.
We can calculate the scale a photograph or map is using by looking at features or landmarks that have standard dimensions. For example if the pool in the following picture is a $25$25 m hotel pool, can you calculate the scale of the photo?
We know in real life the swimming pool is $25$25 m long. In the photo, the same size pool is only $50$50 cm. Therefore the photo is using a scale of $50$50 cm $:25$:25 m, which can also be expressed as $50$50 cm $:2500$:2500 cm. Simplifying this, we can say the photo is using a scale of $1:50$1:50.
When finding the scale ratio of a photo, it important to convert both sides of the ratio into the same units.
Using the same process in reverse, we can calculate distances on a photo or map if we know the scale.
What is the scale of the site map?
We know the scale of the photo is $1:10000$1:10000. If the length of the site is $20$20 cm on the map, then its actual length is $20\times10000$20×10000 cm. Therefore its length is $200000$200000 cm or $2$2 km.
A commercial plane measuring $66$66 metres long is to be represented on a scale model with a scale of $1:100$1:100. Find, in metres, the length of the plane in the scale model.
Give your answer in metres, correct to 2 decimal places.