Let's solve each problem step by step based on the image you described. The worksheet is titled
"Scale Factor and Scale Drawings Review Packet", and it involves finding dimensions after scaling (either reducing or enlarging) using a scale factor.
---
Problem (1):
Find the dimensions of each rectangle after it has been reduced by a scale factor of ½.
Given:
- Rectangle A: 4 in × 8 in
- Rectangle B: 20 cm × 17 cm
####
Solution:
To reduce a shape by a scale factor of ½, multiply each dimension by ½.
Rectangle A:
- Length: $ 4 \times \frac{1}{2} = 2 $ in
- Width: $ 8 \times \frac{1}{2} = 4 $ in
✔ New dimensions:
2 in × 4 in
Rectangle B:
- Length: $ 20 \times \frac{1}{2} = 10 $ cm
- Width: $ 17 \times \frac{1}{2} = 8.5 $ cm
✔ New dimensions:
10 cm × 8.5 cm
---
Problem (2):
Find the dimensions of each rectangle after it has been enlarged by a scale factor of 6.
Given:
- Rectangle C: 18 in × 10 in
- Rectangle D: 6.5 cm × 14 cm
####
Solution:
To enlarge by a scale factor of 6, multiply each dimension by 6.
Rectangle C:
- Length: $ 18 \times 6 = 108 $ in
- Width: $ 10 \times 6 = 60 $ in
✔ New dimensions:
108 in × 60 in
Rectangle D:
- Length: $ 6.5 \times 6 = 39 $ cm
- Width: $ 14 \times 6 = 84 $ cm
✔ New dimensions:
39 cm × 84 cm
---
Problem (3):
Mr. Jones is designing a new patio that is a rectangle. The blueprint drawing of the patio has a length of 11 inches and a width of 11 inches. The blueprint will be enlarged by a scale factor of 10. What will be the dimensions, in inches, of the actual patio?
####
Solution:
The blueprint is being
enlarged by a scale factor of
10, so we multiply both dimensions by 10.
- Length: $ 11 \times 10 = 110 $ inches
- Width: $ 11 \times 10 = 110 $ inches
✔ Final dimensions:
110 inches × 110 inches
> Note: Since the original was a square (11×11), the scaled version is also a square.
---
✔ Summary of Answers:
(1)
- Rectangle A:
2 in × 4 in
- Rectangle B:
10 cm × 8.5 cm
(2)
- Rectangle C:
108 in × 60 in
- Rectangle D:
39 cm × 84 cm
(3)
- Actual patio:
110 in × 110 in
---
🔍 Key Concept Recap:
-
Scale Factor < 1: Reduction (e.g., ½ means half size)
-
Scale Factor > 1: Enlargement (e.g., 6 means 6 times bigger)
- Multiply
all dimensions by the scale factor.
- Units remain the same unless converted.
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of 7th grade math scale factor worksheet.
