Question

Each polygon pair is similar. Find the missing side length

Answer 1

I'll do problem 1 to get you started.

The vertical sides are 3 and x for the left and right figures.

The horizontal sides are 15 and 60 for the left and right figures.

The corresponding sides form fractions which are equal (due to the nature of the similar polygons)

3/x = 15/60

3*60 = x*15 ... cross multiply

180 = 15x

15x = 180

x = 180/15 .... divide both sides by 15

x = 12

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Another way you can see this is note how the jump from 15 to 60 is "times 4", so the jump from 3 to x must also be "times 4" to keep the same proportion

3 ---> x = 3*4 = 12

Or you could set up the proportion

60/15 = x/3

4 = x/3

x/3 = 4

x = 3*4

x = 12

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Final Answer: 12