**To begin with lets consider the scale** **1 : 500 **

**What does this actually mean ?**

It means that **1cm** **on the drawing** actually represents **500cms** **in actual length**

In **ratio format** this will be written as;

**D : AL**

**1 : 500**

This can also be written as **1cm : 5m (WHY?)**

There are **100cm in 1m **

Therefore if we divide the **500cms by 100** we end up with **5m**

Next if we consider the scale **5cm : 1km**

The **" : " **means **"is to"**

Now we will change the **km to cm**

**1km = 1000m = 100 000cm**

There is **1000m in a km** and to change the** m **to** cm **we** multiply by 100**

**So 5cm : 1km** can also be written as **5cm : 100 000cm **(can be simplified)

To simplify we **divide by 5 **which equals **1cm : 20 000cm**

**Therefore 5cm : 1km is equivalent to 1cm : 20 000cm**

**They are equivalent scales**.

**Examples;**

**( i )** The distance between two towns measures **6cm** on a map. What is the true distance if the scale is **1 : 50 000**

The** True Distance = 6cm x 50 000**

** = 300 000cm**

We can simplify this by **dividing **the **300 000 by 100** which gives us **3000m**

and by further **dividing **the** 3000m by 1000** we can simplify this to **3km**

**Therefore the True Distance between the two towns is 3km. **

**So** **\ True Distance = 3km (Answer)**

**( ii )** This next example is **the opposite working of the above,** this time we are looking **the Measurement on the map** as we have been given the** True Distance.**

The **drawing** of an Aircraft uses a scale of **1 : 900**

If the Aircrafts wingspan is **30m what length on the drawing actually represents this?**

**Drawing Length =** **30m **÷ **900**

** = 0.033 m **( **to change 0.033 to mm X 1000**)

** = 33mm**

**Therefore the length on the drawing that represents the wingspan is 33mm.**

**So** **\ LOTD = 33mm **

**The next example shows how to work out a Scale:-**

**( iii )** The plans of a house show a room to be **4.0m X 3.6m. **The **dimensions of the room** **on the plans** **measure 20mm X 18mm.**

**What was the scale used?**

**True Lengths = 4.0m X 3.6m**

**Drawing Lengths = 20mm X 18mm**

**To find out the scale we will use the first part of each of the above equations;**

**DL : TL**

**20mm : 4.0m ( x by 1000 to change to mm)**

**20mm : 4000mm**

**As you can see both parts of the equation are now in mm, so how can we break this down and simplify it.**

**Well we can divide both sides by 20.**

**Therefore;**

** DL : TL**

** 20mm : 4000mm ( ****÷ by 20** )

**= 1mm : 200mm **

**So** **\ TheScale = 1 : 200 ( Answer)**