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

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.

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

Video to watch http://www.virtualnerd.com/pre-algebra/ratios-proportions/scale- models/scale-model-examples/scale-map-distance-example

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.

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.

Watch the video: http://www.virtualnerd.com/pre-algebra/ratios-proportions/similar-figures-indirect-measurement/similar-figures/find-scale-factor-similar-figures 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 1 3 ; The drawing’s scale is 1 in : 3 yds

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. 1 40 = 𝑥 100 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.

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. http://youtu.be/xWN6xl1MAYU

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