How will you measure up?

6x = 84 y = 25
5

Demonstrate the relationship between similar plane figures
Read and use map scales
Interpret and sketch simple scale drawings
Solve problems involving scale drawings

What do these things have in common?

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Scale: The ratio of a set of measurements
Scale factor: The number by which each side of the original object is multiplied to find the corresponding side of the model.
Scale drawing: A drawing of a real object that is proportionally smaller or larger than the real object

The map shown is a scale
drawing. A scale drawing is a drawing of a real object that is proportionally smaller or larger than the real object. In other words, measurements on a scale drawing are in proportion to the measurements of the real object.
A scale is a ratio between two sets of measurements.
In the map above, the scale is 1 in:100 mi . This ratio means that 1 inch on the map represents 100 miles.

The scale factor is 4.
The scale factor for Hot
Wheels® cars is 64:1.

Questions Answers
What is scale factor?
The number used to proportionately enlarge or reduce an object based on the ratio of the length of one pair of corresponding sides.
How do I use scale factor?
1) Write a proportion: One ratio should represent the scale and the other should represent the actual measurements.
2) Solve for the missing piece of information http://www.thefutureschannel.com/dockets/hands-on_math/designing_toy_cars/

The scale on a map is 4 in: 1 mi. On the map, the distance between two towns is 20 in. What is the actual distance?
1 mi
=
_____
x mi
1 • 20 = 4 • x
20 = 4x
20
4
=
___
4
5 = x
5 miles
Write a proportion using the scale.
Let x be the actual number of miles between the two towns.
The cross products are equal.
x is multiplied by 4.
Divide both sides by 4 to undo multiplication.
HINT: Think “4 inches is 1 mile, so 20 inches is how many miles?” This approach will help you set up proportions in similar problems.

On a map of the Great Lakes, 2 cm = 45 km.
Find the actual distance of the following, given their distances on the map.
1. Detroit to Cleveland = 12 cm
2. Duluth to Nipigon = 20 cm
270 km
450 km
3. Buffalo to Syracuse = 10 cm 225 km
4. Sault Ste. Marie to Toronto = 33 cm 742.5 km

Is the Statue of Liberty’s nose too long?
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Can we assume that the
Statue of Liberty is similar in scale to an average person?
Would it be true that the lengths of corresponding body parts should have the same ratio?
Typically your nose is 1/8 the length of your arm, which is the scale factor.

Is the Statue of Liberty’s nose too long?

Using a proportion, determine the length of the Statue of
Liberty’s nose if her arm is 42 feet long.
nose = Lady Liberty’s nose arm Lady Liberty’s arm
 Lady Liberty’s nose, if proportionate, should be 5 1/4 feet long.
 How long is it?
4 1/2 feet long

Practice
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Page 378
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Use the floor plan of the house to find the dimensions of the following rooms. Give length and width of each room in feet:
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Living Room
Bedroom #1
Bedroom #2
Bathroom
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Hall
Kitchen
Length of house
Width of house