Question

the polygons in each pair are similar. find the scale factor of the smaller figure to the larger figure.
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)

Explanation:

Step1: Identify corresponding sides

For each pair, match a side of the smaller figure to the corresponding side of the larger figure, then calculate the ratio (larger side / smaller side).

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Problem 11

Step1: Pick corresponding sides

Smaller side: $4$, Larger side: $24$

Step2: Calculate scale factor

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

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Problem 12

Step1: Pick corresponding sides

Smaller side: $20$, Larger side: $25$

Step2: Calculate scale factor

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

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Problem 13

Step1: Pick corresponding sides

Smaller side: $20$, Larger side: $30$

Step2: Calculate scale factor

$\frac{30}{20} = \frac{3}{2}$

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Problem 14

Step1: Pick corresponding sides

Smaller side: $7$, Larger side: $14$

Step2: Calculate scale factor

$\frac{14}{7} = 2$

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Problem 15

Step1: Pick corresponding sides

Smaller side: $6$, Larger side: $9$

Step2: Calculate scale factor

$\frac{9}{6} = \frac{3}{2}$

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Problem 16

Step1: Pick corresponding sides

Smaller side: $5$, Larger side: $30$

Step2: Calculate scale factor

$\frac{30}{5} = 6$

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Problem 17

Step1: Pick corresponding sides

Smaller side: $35$, Larger side: $42$

Step2: Calculate scale factor

$\frac{42}{35} = \frac{6}{5}$

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Problem 18

Step1: Pick corresponding sides

Smaller side: $20$, Larger side: $30$

Step2: Calculate scale factor

$\frac{30}{20} = \frac{3}{2}$

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Problem 19

Step1: Pick corresponding sides

Smaller side: $35$, Larger side: $42$

Step2: Calculate scale factor

$\frac{42}{35} = \frac{6}{5}$

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Problem 20

Step1: Pick corresponding sides

Smaller side: $7$, Larger side: $35$

Step2: Calculate scale factor

$\frac{35}{7} = 5$

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Answer:

1. $6$
2. $\frac{5}{4}$
3. $\frac{3}{2}$
4. $2$
5. $\frac{3}{2}$
6. $6$
7. $\frac{6}{5}$
8. $\frac{3}{2}$
9. $\frac{6}{5}$
10. $5$