### Scale

**1. Scale Image**

Maps and plans include scale drawings. In this case, the scale is the ratio between the distance on the map and the actual distance.

$$\text{Scale}=\frac{\text{Distance on map}}{\text{real distance}}$$

Example:

The distance between two cities on the map is 6 cm, while the actual distance is 18 km. Determine the scale of the map.

Solution:

Actual distance = 18 km = 1,800,000 cm $$\text{Scale}=\frac{6}{1,800,000}=\frac{1}{300,000}$$ So, The scale of the map is 1 : 300,000, meaning that every 1 cm on the map represents 300,000 cm in actual distance.

**2. Scale Model**

Models are small imitations with the exact shape of the ones being imitated. For example, airplane models and car models. The size comparison in the scaled model is the same as the actual size comparison.

Let the length, width and height of the model respectively are $\displaystyle p_m$, $\displaystyle l_m$ and $\displaystyle t_m$, and the actual length, width and height are $\displaystyle p_a$, $\displaystyle l_a$ and $\displaystyle t_a$, so:

$$\frac{p_m}{p_a}=\frac{l_m}{l_a}=\frac{t_m}{t_a}$$

Example:

A car is 3.6 meters long and 1.6 meters wide. The car will be made a model with a length of 8 centimeters. Determine the width of the car model.

Solution: $$\frac{9}{3.6}=\frac{x}{1.6}$$ $$x=4$$ So, the width of the model car is 4 centimeters.

**3. Scale on Thermometer**

Temperature can be measured using a thermometer. Scales that can be used to measure temperature include the Celsius, Reamur, Fahrenheit and Kelvin scales. The four scales have differences in temperature measurement. The comparison of the Celsius, Reamur, Fahrenheit, and Kelvin scales can be written as follows:

$$\frac{C}{5}=\frac{R}{4}=\frac{F-32}{9}=\frac{K-273}{5}$$

Example:

The temperature in a room is 25 $^\text{o}$C. Express the room temperature on the Reamur scale.

Solution: $$\frac{C}{5}=\frac{R}{4}$$ $$\frac{25}{5}=\frac{R}{4}$$ $$R=20$$

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