1. You will use proportions with Scale drawings.
6.6
You will use proportions with Scale drawings.

2. Vocabulary
A scale drawing is a two-dimensional drawing that is similar to the object it represents.
A scale model is a three-dimensional model that is similar to the object it represents
The scale of a scale drawing or scale model gives the relationship between the drawing or model’s dimensions and the actual dimensions.

3. 𝑠𝑐𝑎𝑙𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑠𝑐𝑎𝑙𝑒 𝑎𝑐𝑡𝑢𝑎𝑙
You must remember….
𝑠𝑐𝑎𝑙𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑠𝑐𝑎𝑙𝑒 𝑎𝑐𝑡𝑢𝑎𝑙
Scale is the drawing and the actual is the real object.
Notice the proportion

4. Video to watch
models/scale-model-examples/scale-map-distance-example

5. The distance on a map (scale) from Toronto, Canada to Ottawa, Canada, 9 cm. The scale is 1 cm : 25 mi.
Let’s look at the ratio:
𝑠𝑐𝑎𝑙𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 so 1 𝑐𝑚 25 𝑚𝑖
Therefore, let’s look at a proportion to find the actual distance. 1𝑐𝑚 25 𝑚𝑖 = 9𝑐𝑚 𝑥 𝑚𝑖
Let’s solve by cross multiplying. 1x = 25 · 9
x = 25 so the actual distance is 225 miles.

6. The scale of a blueprint is 1 in : 3 ft. The actual length of the l
living room is 18 ft. Find the length of the living room on the
blueprint.
𝑠𝑐𝑎𝑙𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 = 𝑠𝑐𝑎𝑙𝑒 𝑎𝑐𝑡𝑢𝑎𝑙 [ 1 𝑖𝑛 3 𝑓𝑡 = 𝑥 𝑖𝑛 18 𝑓𝑡 ] Cross multiply 3 x = 18; x = 6
The length of the living room [scale/blueprint] is 6 inches.

7. Watch the video:
A gardener is making a scale drawing of a garden. The length of the actual garden is 9 yards. The length of the garden in the drawing is 3 inches. Find the drawing’s scale.
3 𝑖𝑛 9𝑦𝑑𝑠 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑠𝑐𝑎𝑙𝑒 𝑑𝑟𝑎𝑤𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝑔𝑎𝑟𝑑𝑒𝑛
3 𝑖𝑛 9 𝑦𝑑𝑠 ; simplify ; The drawing’s scale is 1 in : 3 yds

8. Finding a dimension of a scale model
A model of a building has a scale of 1:40. The building is 100 ft.
tall. Find the height of the model.
= 𝑥 𝐷𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑠 𝑜𝑓 𝑚𝑜𝑑𝑒𝑙 𝐷𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑠 𝑜𝑓 𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔
100 = 40x [cross product]
2.5 = x [Divide each side by 40]
Answer: The height of the model is 2.5 ft.

9. Writing a scale without units:
Watch the following video: the first part of the video explains conversions it is another resource tool. If you feel comfortable with conversions skip the video to 4:08.

10. Practice Problems:
Pg. 302 – 304 # 4, 16, 22, 28, 30, 32, 38 a, 49