7th Grade Math Scale Factor and Scale Drawings Review Packet ... - Free Printable

Let’s solve each problem step by step.

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Part 1: Find the dimensions after reduction by a scale factor of ½

When you reduce a shape by a scale factor, you multiply each dimension by that factor.

#### (1) Original rectangle: 4 in × 6 in
→ Reduced by ½:
- Length: 4 × ½ = 2 in
- Width: 6 × ½ = 3 in
✔ Answer: 2 in × 3 in

#### (3) Original rectangle: 22 cm × 27 cm
→ Reduced by ½:
- Length: 22 × ½ = 11 cm
- Width: 27 × ½ = 13.5 cm
✔ Answer: 11 cm × 13.5 cm

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Part 2: Find the dimensions after enlargement by a scale factor of 6

When you enlarge a shape by a scale factor, you multiply each dimension by that factor.

#### (3) Original rectangle: 18 m × 10 m
→ Enlarged by 6:
- Length: 18 × 6 = 108 m
- Width: 10 × 6 = 60 m
✔ Answer: 108 m × 60 m

#### (4) Original rectangle: 6.5 m × 14 m
→ Enlarged by 6:
- Length: 6.5 × 6 = 39 m
- Width: 14 × 6 = 84 m
✔ Answer: 39 m × 84 m

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Part 3: Mr. Jezer’s patio design

Original blueprint dimensions:
- Length = 6 inches
- Width = 11 inches

Scale factor for enlargement = 25

So, we multiply each dimension by 25:

- New length = 6 × 25 = 150 inches
- New width = 11 × 25 = 275 inches

✔ Answer: The actual patio will be 150 inches long and 275 inches wide.

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## ✔ Final Answers:

(1) 2 in × 3 in
(3) 11 cm × 13.5 cm
(3) 108 m × 60 m
(4) 39 m × 84 m
(5) 150 inches by 275 inches

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💡 Explanation Summary:

- Reduction means multiplying by a fraction less than 1 (like ½).
- Enlargement means multiplying by a number greater than 1 (like 6 or 25).
- Always apply the scale factor to both dimensions (length and width) to keep the shape proportional.

Let me know if you’d like to visualize any of these transformations!