Scale and Scale Factor
EX 2. If the scale is 18:3 then what is the scale factor?
1/6
EX. 8 The actual measurement of the length of a pickup is 14 feet. If a model of the pickup has a scale of 2 inches : 14 feet : what is the scale factor?
1/84
EX. 4. If a map's scale is 3:36 then the scale factor from the map to the original scale is ?
12
EX. 6. If the shortest side of a triangle measures 4 inches and it was enlarged using a scale factor of 3, what would its new length be?
12
EX. 7 If side AB was enlarged by a scale factor of 4. What would its new length be? (enter just the number, not the unit name)
16
EX 12. The scale of a baseball bat to its enlarged replica is 2 inches to 10 feet. If a regular baseball bat is 33 inches, how tall would the replica be?
165 feet
EX 13. Rectangle A has a length of 14 and a width of 9. It is similar to Rectangle B. If rectangle B has a length of 27 what is the width of rectangle B? Round to the nearest tenth.
17.4
EX 11. On a map, 2 inches is 35 miles. The distance between Troy City and Ben City is 315 miles. How far apart are they on the map?
18 inches
EX 6. A picture of a cake has a measurement of 8 inches across. Using a scale factor of 2:5, how many inches across is the actual cake?
20 inches
EX. 10 The dimensions of a room on a scale drawing are 6cm by 7cm. If the scale of the drawing is 2cm : 5 meters, what is the area of the actual room?
262.5 square meters Hint: Create a proportion for each dimension of the room. Use the scale 2/5 for the first ration. After finding both dimensions multiply them together to find the area of the room. **don't forget your units!
EX 3. If the constant of proportionality is 3, then what is the scale factor?
3
EX.1 If the scale is 4:20 then the scale factor is ?
5
EX. 9 The picture of a car has a scale of 1 inch to 3 feet. If the picture measures 3 inches across, then how many feet long is the actual car?
9 ft
Ratio
A comparison of two quantities by division
Scale Drawing
A drawing that uses a scale to make an object proportionally smaller than or larger than the real object. Drawings are reduced or enlarged by a certain amount called the scale factor. EX-a blueprint is a scale drawing of a house.
Scale Model
A figure that is larger or smaller than the original object. A model airplane is a replica of a real plane. Both examples are proportional to the actual object.
Scale Factor
A ratio that compares the sizes of the parts of one figure or object to the sizes of the corresponding parts of a similar figure or object. Scale Factor is also referred to as the multiplier and the constant of proportionality.
Englarement
A scale factor that results in a larger copy. Ex taking a picture to the store to have it printed in a larger size.
Reduction
A scale factor that results in a smaller copy. Ex. drawing a map of the school.
Proportion
An equation that state that two ratios are equal
Corresponding Sides
Corresponding sides are sides that are in the same position in similar figures.
Similar Figures
Figures that have the same shape (congruent angles) and proportional sides.
F. How do you calculate Scale Factor?
Option 1)Create a ratio- scale drawing:original. What would you have to multiply the scale drawing by to equal the original object? Option 2)formula-Divide original object by the scale.
Scale
The ratio between 2 sets of measurements of two similar geometric figures. EX: A postcard has a scale of 5 in to 12 feet with the scene that is depicts. That means every 5 inches in the postcards equals 12 feet in real life. The scale may also be presented in the problem as "5:12" or "5 to 12"
F. How do you calculate Scale?
To find the missing value in a scale comparison create a proportion. Fill in your 2 fractions. The first is your known scale (ex 3:7 would be 3/7). The second fraction will have an known quantity and and unknown quantity that you will represent using a variable. Set your fractions equal to each other. Scale over original equals scale over original. Using cross multiplication, solve for the unknown quantity. **Remember to compare similar parts!
Equivalent Ratios
Two ratios that describe the same relationship
Proportional
Figures or equations have the same scale factor (multiplier).