Grade 9 Similarity & Scale worksheet
from Gradelings · Name: ______________________
How to explain it
- Similar shapes have the same shape but different sizes.
- The scale factor is new length ÷ old length.
- Multiply every length by the scale factor. Areas change by the factor squared.
Example: A rectangle 4 cm by 6 cm is enlarged by a scale factor of 3. What are the new sides? 4 × 3 = 12. 6 × 3 = 18. Answer: 12 cm by 18 cm
Question 1
Triangle B is an enlargement of triangle A. A side of 2 cm on triangle A matches a side of 10 cm on triangle B. What is the scale factor?
answer box
5
Hint: Scale factor = new length ÷ original length = 10 ÷ 2 = 5.
Question 2
Two rectangles are similar. The small one is 8 cm by 5 cm. The large one is 24 cm long. How wide is the large rectangle?
answer boxcm
15 cm
Hint: The scale factor is 24 ÷ 8 = 3. Multiply the width by 3: 5 × 3 = 15 cm.
Question 3
△ABC ~ △DEF. AB = 6 cm, BC = 8 cm and DE = 18 cm. How long is EF?
answer boxcm
24 cm
Hint: The sides are in proportion: DE/AB = EF/BC, so EF = 8 × (18/6) = 8 × 3 = 24 cm.
Question 4
A 3 m stick casts a 2 m shadow. At the same time, a tree casts a 12 m shadow. How tall is the tree?
answer boxm
18 m
Hint: The triangles are similar, so height ÷ shadow stays the same: tree = 3 × 6 = 18 m.
Question 5
A scale drawing uses 1 cm for every 20 cm in real life. A wall measures 11 cm on the drawing. How long is the real wall in centimetres?
answer boxcm
220 cm
Hint: Multiply by the scale: 11 × 20 = 220 cm.
Question 6
A cube is enlarged by a scale factor of 4. By what factor does its volume grow?
answer box
64
Hint: Volume uses three lengths, so it grows by 4³ = 64.
Question 7
Rectangle 1 is 4 cm by 10 cm and Rectangle 2 is 8 cm by 20 cm. Are they similar?
- Yes
- No
Yes
Hint: Compare the ratios: 8 ÷ 4 = 2 and 20 ÷ 10 = 2. Both sides are multiplied by the same number, so they are similar.
Question 8
A scale factor less than 1 makes a figure…
- larger (an enlargement)
- negative
- the same size
- smaller (a reduction)
smaller (a reduction)
Hint: Multiplying by a number below 1 shrinks lengths.
Question 9
Triangle B is an enlargement of triangle A. A side of 5 cm on triangle A matches a side of 10 cm on triangle B. What is the scale factor?
answer box
2
Hint: Scale factor = new length ÷ original length = 10 ÷ 5 = 2.
Question 10
Two rectangles are similar. The small one is 10 cm by 5 cm. The large one is 20 cm long. How wide is the large rectangle?
answer boxcm
10 cm
Hint: The scale factor is 20 ÷ 10 = 2. Multiply the width by 2: 5 × 2 = 10 cm.
Answer key
- 1. 5
- 2. 15 cm
- 3. 24 cm
- 4. 18 m
- 5. 220 cm
- 6. 64
- 7. Yes
- 8. smaller (a reduction)
- 9. 2
- 10. 10 cm
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