Using Scale

A scale is a ratio or proportion that shows the relationship between the length of a drawing and the corresponding length of the actual object. 

In scale drawing:

1. All lengths must be in proportion to the corresponding length of the actual object, and 

2. All angles must be drawn to the corresponding angles on the actual object. 

For example, a scale of 1 : 3 means 1 on the scale drawing represents the size of 5 on the actual drawing.

Forms of writing scales” 

a. 1 cm represents 10 m 

b. 1 cm to 10 m 

c. 1 cm : 10 m or 1: 10

d. \( \frac{1 }{10} \)

Example 1.1.1:

A rectangle is drawn to a scale of 1 cm to 10 cm. If the length of the scaled rectangle is 80 cm, what is the length of the actual object? 

Solution: 

Length of the rectangle on scale drawing = 80 cm 

Length of the rectangle on actual object = x cm

Scale = \( \frac{any \: length \: of \: scale \: drawing }{corresponding \: length \: of \: actual \: object} \)

Scale	Actual Object
1 cm	10 cm
80 cm	x cm

∴ \( \frac{1\: cm}{80 \: cm} = \frac{10\: cm}{x \: cm} \)

cross multiply

\( \scriptsize x \: \times \: 1\:cm = 80\:cm \: \times \: 10\:cm \)

x = \( \frac{800\:cm^2}{1\:cm}\\ \)

x = \( \frac{800\:cm \: \times \: cm}{1\:cm}\)

x = \( \frac{800\:cm \: \times \: \not{cm}}{1\: \not{cm}}\)

x = \(\scriptsize 800\:cm \)

The length of the actual object (x) is 800 cm

Example 1.1.2:

A triangle is drawn to a certain scale. If the length of the base of the scaled triangle is 80 cm, and the length of the base of the actual triangle is 800 cm, what is the scale? 

Solution 

Length of base on scale drawing = 80 cm 

Length of base on actual object = 800 cm

Scale = \( \frac{any \: length \: on \: scale \: drawing }{corresponding \: length \: on \: actual \: object} \)

Scale = \( \frac{80\:cm }{800\:cm} \\ = \frac{8}{80} \\ = \frac{1}{10} \\ = \scriptsize 1\::\:10 \)

= 1 cm to 10 cm 

= 1 cm represents 10 cm 

Evaluation: