A scale drawing is a two-dimensional drawing of an object that is proportional to the object. A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units. A scale model is a three-dimensional model that is proportional to the object.
Under a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length? Class Example Write a proportion using the scale. Let x be the actual length of the amoeba. 1000 x = 1 8The cross products are equal. x = 0.008 The actual length of the amoeba is eight thousandths of a millimeter. 1000 1 = 8 mm x mm Solve the proportion.
Under a 10,000:1 microscope view, a fiber appears to have length of 1 mm. What is its actual length? Partner Practice Write a proportion using the scale. Let x be the actual length of the fiber. 10,000 x = 1 1The cross products are equal. x = 0.0001 The actual length of the fiber is 1 ten- thousandths of a millimeter. 10,000 1 = 1 mm x mm Solve the proportion.
Scale factor is the ratio of a length on a scale drawing or model to the corresponding length on the actual object. The scale a:b is read “a to b.” For example, the scale 1 cm:4 m is read “one centimeter to four meters.” Reading Math When finding a scale factor, you must use the same measurement units. You can use a scale factor to find unknown dimensions.
The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale? Class Practice 1 cm x m = 4 cm 12 m Set up proportion using scale length. actual length 1 12 = x 4Find the cross products. 12 = 4x Divide both sides by 4. The scale is 1 cm:3 m. 3 = x
A model of a 27 ft tall house was made using a scale of 2 in.:3 ft. What is the height of the model? Partner Practice Find the scale factor. The scale factor for the model is. Now set up a proportion. 1 18 2 in. 3 ft = 2 in. 36 in. = 1 in. 18 in. = 1 18 324 = 18h Convert: 27 ft = 324 in. Find the cross products. 18 = h The height of the model is 18 in. Divide both sides by 18. 1 18 = h in. 324 in. Convert to same measurements What is “h”???Let h equal the height of the model.
A DNA model was built using the scale 5 cm: 0.0000001 mm. If the model of the DNA chain is 20 cm long, what is the length of the actual chain? Individual Practice The scale factor for the model is 500,000,000. This means the model is 500 million times larger than the actual chain. 5 cm 0.0000001 mm 50 mm 0.0000001 mm == 500,000,000 Find the scale factor.
Individual Practice...continued 500,000,000 1 20 cm x cm =Set up a proportion. 500,000,000x = 1(20) x = 0.00000004 The length of the DNA chain is 4 10 -8 cm. Find the cross products. Divide both sides by 500,000,000.
How is scale different than rate? Discuss with your partner Write an answer (in words)
Sometimes, distances cannot be measured directly. One way to find such a distance is to use indirect measurement, a way of using similar figures and proportions to find a measure.
Class Practice Triangles ABC and EFG are similar. Find the length of side EG. B AC 3 ft 4 ft F E G 9 ft x = Set up a proportion. Substitute 3 for AB, 4 for AC, 9 for EF, and x for EG. 3x = 36Find the cross products. 3 4 = 9 x 3x3x 3 = 36 3 Divide both sides by 3. AB AC EF EG The length of side EG is 12 ft. Divide both sides by 3. x = 12
Individual Practice Triangles DEF and GHI are similar. Find the length of side HI. 2 in E DF 7 in H G I 8 in x DE EF = GH HI Set up a proportion. Substitute values for DE, EF, GH, and HI. 2x = 56 The length of side HI is 28 in. x = 28 2 7 = 8 x 2x 2 = 56 2 Find the cross products and solve for x.