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Scale Factors, Scale Drawings, Scale Drawings, Scale Drawings, Proportional Reasoning & Scale Factor

Terms in this set (82)

similar figures
have the same shape but not the same size
scale drawing
a drawing that uses a scale to make an object smaller than or longer than the real object.
scale
the ratio between two sets of measurements.
scale factor
the ratio used to enlarge or reduce similar figures.
scale model
a proportional model of a three-dimensional figure object.
similar
figures with the same shape but not necessarily the same size are similar
corresponding sides
matching sides of two or more polygons.
corresponding angles
angles in the same relative position in polygons with an equal number of sides.
proportions
if you know 2 figures are similar, you can find unknown lengths of sides, as well as find unknown angle measurements
Scale Drawing
A proportional two-dimensional drawing of an object.
Scale
A ratio between 2 sets of measurements.
Unit rate
A rate in which the second quantity in the comparison is one.
2.8
Julio walks 3.5 miles in 1.25 hours. Find the unit rate
.5
A garden snail moves one-sixth foot in one-third hour. Find the unit rate.
24.75
A scale drawing of a billboard uses the scale 4 cm:9 ft. The length of the billboard in the drawing is 11 cm. How long is the actual billboard?
19.5 by 36
A bookcase measures 13 feet wide and 24 feet tall. What would the bookcase's measurements be on a scale drawing using the scale
3 cm:2 ft?
15
Bob makes a scale drawing of a statue using the scale 1 cm:5 ft. His drawing measures 12 cm. Kia makes a scale drawing of the same statue using the scale 1 cm:4 ft. How many centimeters tall is the statue in Kia's drawing?
96
Jorge's printer can print 24 pages in 15 minutes. How many pages can it print in 1 hour?
5980
Richard estimates that he can apply
fertilizer to 4,485 square feet of grass
in three-fourths an hour. How many square feet of 4
grass can Richard fertilize per hour?
Ratio
A comparison of two quantities by division
Rate
A ratio that compares two quantities measured in different units.
proportional
An equation that states that two ratios are equivalent.
Proportional Relationship
A relationship between two quantities in which the ratio of one quantity to the other quantity is equal.
Radius
A line segment with one endpoint at the center of a circle and the other endpoint on the circle
Diameter
A line segment that passes through the center of a circle and has endpoints on the circle.
Area
The number of square units needed to cover a given surface.
Asymmetry
Not identical on either side of a central line.
Symmetrical
Identical on either side of a central line.
Circle
The set of all points in a plane that are the same distance from a given point called the center.
Circumference
The distance around the circle.
Triangle
A three-sided polygon.
Rectangle
A parallelogram with four right angles.
Square
A rectangle with four congruent lines.
Trapezoid
A quadrilateral with exactly on pair of parallel sides.
blueprint
a detailed outline or plan for a building
dilation
a proportional enlargement or reduction of a figure through a point
dimensions
measurements in width, length, and sometimes depth
proportion
an equation that states two ratios are equal
ratio
a comparison of two quantities by division
scale
a ratio between two sets of measurements
scale drawing
a drawing that uses a scale to make an object smaller than or larger than the real object
scale factor
the ratio used to enlarge or reduce two similar figures
84 inches
On a scale drawing, the scale factor is 1/12. A plum tree is 7 inches tall on the scale drawing. What is the actual height of the tree?
75 miles
On a road map, the distance between 2 citites is 2.5 inches. The map scale is 1 inch = 30 miles. What is the actual distance between the cities?
129 miles
Ms. Jackson is driving from South Bend to Indianapolis. She measures a distance of 4.3 cm between the cities on her map. What is the actual distance between the cities if the map scale is 1 cm = 30 miles?
135 inches
On a scale drawing, a tree is 6 3/4 inches tall. The scale factor is 1/20. Find the height of the actual tree.
190 miles
On a road map of Virginia, the distance from Alexandria to Roanoke is 7.6 cm. What is the actual distance between the cities if the map scale is 2 cm = 50 miles?
1,100 miles
The scale on a road map is 1 cm = 500 miles. If the distance on the map between New York City and Memphis is 2.2 cm, what is the actual distance between the two cities?
1.04 feet
There are several different scales in model railroading. Trains designated as O gauge are built to a scale factor of 1:48. To the nearest hundredth of a foot, how long is a model of a 50 foot boxcar in O gauge?
156.5 cm
For a school project, LeeAnn is making a model of the Empire State Building. She is using a scale of 1 cm = 8 feet. The Empire State Building is 1,252 feet tall. How tall is her model?
60 inches
The scale factor for Maria's dollhouse furniture is 1:8. If the sofa in Maria's dollhouse is 7 1/2 inches long, how long is the actual sofa?
3.5 inches
Josh wants to add a model of a tree to his model railroad layout. How big should the model tree be if the actual tree is 315 inches and the scale is 1:90?
1.8 miles
The scale on a wall map is 1 inch = 55 miles. What is the distance on the map between 2 cities that are 99 miles apart?
9 feet
On a blueprint, the scale is 1/2 inch = 10 feet. What is the actual height of the living room which is 9/20 inch on the blueprint?
29 inches
If 1 inch = 55 miles on a map, then how many inches will represent 1595 miles on the map?
4.25 inches
If a building's actual length is 34 feet, what would it's size be on a scale drawing? The scale is 1 inch = 8 feet
25 inches
The Empire State Building is 1250 feet tall. How tall would the building be on a scale model if the scale is 1 inch = 50 feet?
26 cm
The Eiffel Tower is 312 meters tall. How tall would the building be on a scale model if the scale is 1 cm = 12 m
ratio
the comparison of two numbers
rate
the ratio comparing values of two different units
unit rate
the ratio comparing one value to 1
proportion
two ratios that are equal
scale factor
A number you multiply one figure by to get an enlargement or reduction.
enlargement
Scale factor greater than 1 results in this.
reduction
Scale factor less than one results in this.
$0.05
$2.69 for 54 paper plates. Find the unit rate.
$0.97
12 pound turkey for $11.64. Find the unit rate.
$1.89
10 pound ham for $18.89. Find the unit rate.
$0.19
$2.29 for 12 oz of Cranberries. Find the unit rate.
$.04
$1.99 for 5 pound bag of potatoes. Find the unit rate.
$0.15
$1.79 for 12 count of Dinner Rolls. Find the unit rate.
$0.25
$2.99 for 12 pack of Coke. Find the unit rate.
1/4
What is the scale factor from a large figure with a length of 20 inches to a mathematically similar figure with a length of 5 inches?
30
What is the scale factor from a figure with a height of 10 cm to a similar figure with a height of 300 cm?
2.08
Find the scale factor for two similar rectangles. The first rectangle has a width of 25 and the second, similar rectangle has a width 52.
4
A detective needs to take a closer look at a set of fingerprints. To do this, he has to enlarge the fingerprints to see the details of the actual fingerprint. The actual fingerprint has a height of ¾ of an inch. The enlarged image has a height of 3 inches. What is the scale factor?
1/28
John is building a miniature model of a shed that he has in his backyard. The length of the model shed is 2 inches whereas the actual length of the shed is 56 feet. What is the scale factor from the actual shed to the model?
75
A model of a building is made so that 6 inches represents 30 feet. What is the height of the actual building if the height of the model is 14 inches?
286
There is a small legend on the corner of a scale drawing of the mall states 2 inches of length corresponds to an actual length of 50 feet. If the store measures 11 inches on the scale drawing, how long is the actual store?
8
If the sides of a rectangle are 2 by 5 and the sides of another rectangle are 16 by 40, what is the scale factor?
Scale Drawing
An image or figure that is similar to the original
Similar Figures
Same size, different shape.
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