Grade 9 · Math · Unit 6 of 8
Similarity & Scale
Scale factors and similar figures
What your child practises
Using scale factors to find missing sides, solving shadow and scale-drawing problems, and seeing how enlarging a shape changes its area and volume.
BC Curriculum learning standard: Spatial proportional reasoning: similar shapes, scale factors and scale drawings
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
Triangle B is an enlargement of triangle A. A side of 2 cm on triangle A matches a side of 6 cm on triangle B. What is the scale factor?
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3
Hint: Scale factor = new length ÷ original length = 6 ÷ 2 = 3.
Question 2
Two rectangles are similar. The small one is 4 cm by 2 cm. The large one is 8 cm long. How wide is the large rectangle?
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4 cm
Hint: The scale factor is 8 ÷ 4 = 2. Multiply the width by 2: 2 × 2 = 4 cm.
Question 3
△ABC ~ △DEF. AB = 3 cm, BC = 9 cm and DE = 6 cm. How long is EF?
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18 cm
Hint: The sides are in proportion: DE/AB = EF/BC, so EF = 9 × (6/3) = 9 × 2 = 18 cm.
Question 4
A 1 m stick casts a 2 m shadow. At the same time, a tree casts a 16 m shadow. How tall is the tree?
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8 m
Hint: The triangles are similar, so height ÷ shadow stays the same: tree = 1 × 8 = 8 m.
Question 5
A scale drawing uses 1 cm for every 5 cm in real life. A wall measures 10 cm on the drawing. How long is the real wall in centimetres?
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50 cm
Hint: Multiply by the scale: 10 × 5 = 50 cm.
Question 6
A cube is enlarged by a scale factor of 3. By what factor does its volume grow?
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27
Hint: Volume uses three lengths, so it grows by 3³ = 27.