Scale drawings and scale ratios
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.
Calculating scale
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?
Swimming pool scale (Source: http://taxdollars.blog.ocregister.com/)
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.
Calculating distances
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?
Scaled Site Plan (Source: http://www.arcadiawoods.com.au/media/siteplan-large.jpg)
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.
Practice questions
Question 1
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.