Question

geometry
name
id:
4.14 part 2 - scale factors
date
period
the polygons in each pair are similar. find the missing side length.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)

Explanation:

Step1: Find scale factor

For similar polygons, scale factor $k = \frac{\text{corresponding side of small polygon}}{\text{corresponding side of large polygon}}$ (or vice versa, depending on which is the reference). Then use $k$ to find the missing side.

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Problem 1

Step1: Calculate scale factor

$k = \frac{8}{16} = \frac{1}{2}$

Step2: Find missing side

$\text{Missing side} = 5 \div \frac{1}{2} = 10$

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Problem 2

Step1: Calculate scale factor

$k = \frac{20}{15} = \frac{4}{3}$

Step2: Find missing side

$\text{Missing side} = 12 \div \frac{4}{3} = 9$

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Problem 3

Step1: Calculate scale factor

$k = \frac{24}{30} = \frac{4}{5}$

Step2: Find missing side

$\text{Missing side} = 25 \times \frac{4}{5} = 20$

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Problem 4

Step1: Calculate scale factor

$k = \frac{6}{12} = \frac{1}{2}$

Step2: Find missing side

$\text{Missing side} = 8 \times \frac{1}{2} = 4$

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Problem 5

Step1: Calculate scale factor

$k = \frac{15}{20} = \frac{3}{4}$

Step2: Find missing side

$\text{Missing side} = 21 \div \frac{3}{4} = 28$

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Problem 6

Step1: Calculate scale factor

$k = \frac{32}{40} = \frac{4}{5}$

Step2: Find missing side

$\text{Missing side} = 20 \times \frac{4}{5} = 16$

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Problem 7

Step1: Calculate scale factor

$k = \frac{6}{3} = 2$

Step2: Find missing side

$\text{Missing side} = 4 \times 2 = 8$

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Problem 8

Step1: Calculate scale factor

$k = \frac{24}{6} = 4$

Step2: Find missing side

$\text{Missing side} = 7 \times 4 = 28$

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Problem 9

Step1: Calculate scale factor

$k = \frac{30}{12} = 2.5$

Step2: Find missing side

$\text{Missing side} = 10 \times 2.5 = 25$

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Problem 10

Step1: Calculate scale factor

$k = \frac{20}{25} = \frac{4}{5}$

Step2: Find missing side

$\text{Missing side} = 30 \times \frac{4}{5} = 24$

Answer:

1. $\boldsymbol{10}$
2. $\boldsymbol{9}$
3. $\boldsymbol{20}$
4. $\boldsymbol{4}$
5. $\boldsymbol{28}$
6. $\boldsymbol{16}$
7. $\boldsymbol{8}$
8. $\boldsymbol{28}$
9. $\boldsymbol{25}$
10. $\boldsymbol{24}$