Similar shapes: missing lengths

The Maths Habit

Sam makes a 3 cm by 2 cm rectangle bigger by adding 4 cm to each side. He gets 7 cm by 6 cm. Is it the same shape?

No: 3 by 2 is long and thin, 7 by 6 is nearly a square

What is the scale factor?

3 cm becomes 12 cm 4

A length of 5 cm is enlarged by scale factor 3.
How long is it now?

15 cm

Similar: The same shape, but a different size.
Scale factor: The number every length is multiplied by.

A

3 cm2 cm

B

9 cm6 cm

A and B are similar. Find the missing length.

A

6 cm5 cm

B

12 cm?

A and B are similar. Find the missing length.

A

7 cm3 cm

B

14 cm?

	Width	Height
A	7	3
B	14	6

↩×2

A and B are similar. Find the missing length.

A

9 cm4 cm

B

27 cm?

	Width	Height
A	9	4
B	27	12

↩×3

A and B are similar. Find the missing length.

A

7 cm3 cm

B

14 cm?

	Width	Height
A	7	3
B	14	6

↩×2

A and B are similar. Find the missing length.

A

8 cm5 cm

B

32 cm?

	Width	Height
A	8	5
B	32	20

↩×4

A and B are similar. Find the missing length.

A

7 cm3 cm

B

14 cm?

	Width	Height
A	7	3
B	14	6

↩×2

A and B are similar. Find the missing length.

A

4 cm3 cm

B

12 cm?

	Width	Height
A	4	3
B	12	9

↩×3

A and B are similar. Find the missing length.

A

7 cm3 cm

B

14 cm?

	Width	Height
A	7	3
B	14	6

↩×2

A and B are similar. Find the missing length.

A

?3 cm

B

24 cm12 cm

	Width	Height
A	6	3
B	24	12

↩×4

A and B are similar. Find the missing length.

A

7 cm3 cm

B

14 cm?

	Width	Height
A	7	3
B	14	6

↩×2

A and B are similar. Find the missing length.

A

7 cm2 cm

B

?10 cm

	Width	Height
A	7	2
B	35	10

↩×5

A and B are similar. Find the missing length.

A

?5 cm

B

28 cm20 cm

Similar shapes: missing lengths worksheet, page 1

Similar shapes: missing lengths worksheet, page 2

Answer sheet

A photo is 10 cm by 15 cm. It is enlarged so that its shorter side is 25 cm. How long is its longer side?
37.5 cm
One rectangle is 2 cm by 3 cm. Another is 4 cm by 5 cm. Are they similar? How do you know?
No

A and B are similar rectangles. Find the missing length.
15 cm
Rectangle B is 24 cm by 36 cm. Rectangle A is similar to B, and its shorter side is 6 cm. Find its longer side.
9 cm
Rectangle P is 4 cm by 6 cm. Rectangle Q is 6 cm by 8 cm. Zara says they are similar. Is she right? Explain.
No: 4 × 1.5 = 6 but 6 × 1.5 = 9, not 8

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