Math 6 Honors ( Periods 1, 2, & 3)

Scale Drawing 7-9

Using the book’s drawing on page 237, find the length and width of the room shown, if the scale of the drawing is 1cm: 1.5 m

Measuring the drawing, we find that it has a length of 4 cm and a width of 3 cm
Method 1: write a proportion for the length
Let l = the actual length
1/1.5 = 4/ l
l= 4 (1.5)
l = 6
The room is 6 m long
Write a proportion for the width
Let w = the actual width
1/1.5 = 3/w
w = 3 (1.5)
w = 4.5 m
The room is 4.5 m wide

A scale drawing is a diagram of an object where its length and width aare proportional to the actual length and width.

The scale for the drawing gives the relationship between the drawing's measurements and the actual measurements.
For example 1 inch represents 2 feet

The Scale Factor is the ratio of the length in the drawing to the corresponding actual lenth.

A Scale Factor on a matchbox car of 1/64 would mean that every part of the matchbox car was 1/64 of the actual car-- the windshield, the door, the wheels, the roof... would all have the same relationship.

Scale Factor MUST HAVE the same units of measurements.



Method 2 : Use the scale ratio

1 cm/ 1.5 m = 1/cm/150 cm = 1/150
You need to change the units to the same and then set up a ratio

The actual length is 150 times the length in the drawing so
l =150 (4) = 600 cm = 6 m
w =150 (3) = 450 cm = 4.5 m

The scale on a map is 1 cm to 240 m


Open your books to Page 237, you will notice a drawing of a house. In this drawing of the house, the actual height of 9 meters is represented by a length of 3 centimeters, and the actual length of 21 meters is represented by a length of 7 centimeters.
This means that 1 cm in the drawing represents 3 m in the actual building. Such a drawing in which all lengths are in the same ratio to actual lengths is called a scale drawing.
The relationship of length in the drawing to actual length is called the scale. In the drawing of the house the scale is 1cm: 3m

We can express the scale as a ratio, called the scale ratio, if a common unit of measure is used. Since 3 m = 300 cm, the scale ratio is 1/300

The distance from Ryan’s house to his school is 10 cm on the map. What is the actual distance?
let d = the distance from Ryan’s house to school
1/240 = 10/d so d = 240(10)
d = 2400m or
The distance from Ryan's house to school is 2.4 km


A picture of an insect has a scale 7 to 1. The length of the insect in the picture is 5.6 cm. What is the actual length of the insect?
Let l = the actual length of the insect

7/1 = 5.6/ l
7l = 5.6
l = .8 cm
The actual length of the insect is 0.8 cm which is 8 mm