What if you were told that a scale model of a python is in the ratio of 1:24? If the model measures 0.75 feet long, how long is the real python? After completing this Concept, you'll be able to solve problems like this one by using a proportion.
Watch This
First watch this video.
Now watch this video.
James Sousa: Applications of Proportions
Finally, watch this video.
James Sousa: Using Similar Triangles to Determine Unknown Values
Guidance
A proportion is two ratios that are set equal to each other. Usually the ratios in proportions are written in fraction form. An example of a proportion is
Corollary #1: If
Corollary #2: If
Corollary #3: If
Corollary #4: If
Corollary #5: If
Example A
Solve the proportions.
a)
b)
c)
Remember, to solve a proportion, you need to crossmultiply.
a)
b)
c)
Example B
Your parents have an architect’s drawing of their home. On the paper, the house’s dimensions are 36 in by 30 in. If the shorter length of the house is actually 50 feet, what is the longer length?
To solve, first set up a proportion. If the shorter length is 50 feet, then it lines up with 30 in, the shorter length of the paper dimensions.
Example C
Suppose we have the proportion
First of all, we know this is a true proportion because you would multiply

214=535 
355=142 
52=3514
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Guided Practice
1. In the picture,
Find the measures of
2. In the picture,
3. In the picture,
Answers:
1. Plug in the lengths of the sides we know.
2. Substitute in the lengths of the sides we know.
3. Substitute in the lengths of the sides we know.
Explore More
Solve each proportion.

x10=4235 
xx−2=57 
69=y24 
x9=16x 
y−38=y+65 
20z+5=167  Shawna drove 245 miles and used 8.2 gallons of gas. At the same rate, if she drove 416 miles, how many gallons of gas will she need? Round to the nearest tenth.
 The president, vicepresident, and financial officer of a company divide the profits is a 4:3:2 ratio. If the company made $1,800,000 last year, how much did each person receive?
Given the true proportion,

10y=x6 
1510=d6 
6+1010=y+xx 
15x=yd
For questions 1316,
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