Free Collection of Scale Factor Worksheets | WorksheetZone - Free Printable

Let's solve each problem step by step. Since the figures are similar, their corresponding sides are proportional, and the scale factor is the ratio of the lengths of corresponding sides from the original figure (left) to the image (right).

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1.) Rectangles A and B

- Rectangle A: 9 and 13
- Rectangle B: 90 and 130

We find the scale factor $ s = \frac{\text{side of B}}{\text{side of A}} $

Check both pairs:

- $ \frac{90}{9} = 10 $
- $ \frac{130}{13} = 10 $

✔ Both ratios are equal.

So,
$$
s = \frac{90}{9} = 10
$$

Answer:
$$
\boxed{s = 10}
$$

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2.) Quadrilaterals C and D

- Figure C: sides 7, 7, 4
- Figure D: sides 91, 91, 52

Corresponding sides:
- $ \frac{91}{7} = 13 $
- $ \frac{52}{4} = 13 $

✔ All ratios are consistent.

So,
$$
s = \frac{91}{7} = 13
$$

Answer:
$$
\boxed{s = 13}
$$

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3.) Line segments G and H

- Segment G: length = 14
- Segment H: length = 112

Scale factor:
$$
s = \frac{112}{14} = 8
$$

Answer:
$$
\boxed{s = 8}
$$

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4.) Trapezoids

- Left trapezoid: base = 3, height = 1.5
- Right trapezoid: base = 8, height = 4

Check ratios:

- $ \frac{8}{3} \approx 2.666... $
- $ \frac{4}{1.5} = \frac{40}{15} = \frac{8}{3} \approx 2.666... $

So,
$$
s = \frac{8}{3}
$$

Answer:
$$
\boxed{s = \frac{8}{3}}
$$

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5.) Triangles ABC and DEC (overlapping)

We are given:
- AB = 3.5
- ED = 8.75

These are corresponding sides (since angles at A and D are right angles, and the triangles are similar).

So,
$$
s = \frac{ED}{AB} = \frac{8.75}{3.5}
$$

Simplify:
$$
\frac{8.75}{3.5} = \frac{875}{350} = \frac{175}{70} = \frac{35}{14} = \frac{5}{2} = 2.5
$$

Alternatively:
$$
8.75 ÷ 3.5 = 2.5
$$

✔ So, scale factor is $ 2.5 $ or $ \frac{5}{2} $

Answer:
$$
\boxed{s = \frac{5}{2}} \quad \text{or} \quad \boxed{2.5}
$$

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✔ Final Answers:

1.) $ s = 10 $
2.) $ s = 13 $
3.) $ s = 8 $
4.) $ s = \frac{8}{3} $
5.) $ s = \frac{5}{2} $ or $ 2.5 $

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Summary Table:

| Problem | Scale Factor |
|--------|--------------|
| 1 | 10 |
| 2 | 13 |
| 3 | 8 |
| 4 | $ \frac{8}{3} $ |
| 5 | $ \frac{5}{2} $ |

Let me know if you'd like these written out on the worksheet format!