Here, you will see how scales are used in blueprints. We can have a blueprint for lots of things, for example a house, a room, or the parts of an iPhone.

For a blueprint to be practical, we need to choose a scale that fits the thing we want to make a blueprint of. Things that are very small have to be drawn larger, while very large things have to be drawn smaller, just like we did with the maps.

In the figure above, you can see a blueprint of a living room with a scale of $1:100$. It’s practical to use a blueprint like this when you redecorate your house, just to see how you can place your furniture.

Example 1

**A room is drawn with a scale of $1:100$. The sofa is $\text{}2.5\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$ in the blueprint. How long is that in real life? **

$$\begin{array}{llll}\hfill 2.5\phantom{\rule{0.17em}{0ex}}\text{cm}\cdot 100& =250\phantom{\rule{0.17em}{0ex}}\text{cm}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =(250\xf7100)\phantom{\rule{0.33em}{0ex}}\text{m}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =2.5\phantom{\rule{0.17em}{0ex}}\text{m},\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$ which means the sofa is $2.5$ meters long in real life.

Example 2

**You have been given a model car for Christmas. On the box it says that the car is made with a scale of $1:45$. The car you got is $\text{}10\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$ long. How long is the car in real life? **

$$\begin{array}{llll}\hfill 10\phantom{\rule{0.17em}{0ex}}\text{cm}\cdot 45& =450\phantom{\rule{0.17em}{0ex}}\text{cm}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =(450\xf7100)\phantom{\rule{0.33em}{0ex}}\text{m}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4.5\phantom{\rule{0.17em}{0ex}}\text{m},\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$ which means that the real car is $4.5$ meters long.

Example 3

**You have captured a tadpole and want to examine it. You look online and find a drawing with a scale of $10:1$. In reality the tadpole is $\text{}1.8\text{}\phantom{\rule{0.17em}{0ex}}\text{cm}$ long. How long is the tadpole in the drawing? **

$$1.8\phantom{\rule{0.17em}{0ex}}\text{cm}\cdot 10=18\phantom{\rule{0.17em}{0ex}}\text{cm},$$ |

which means that the tadpole in the drawing is $18$ cm long.