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Scale Factor effects on Length and Perimeter
Contributed by: Mousser
(Original author: Cason)

The ratio of the lengths of corresponding sides in

similar figures (same shape but different size) is

called scale factor.  It may be expressed as a

fraction, decimal, percent, or whole number. 

 

The scale factor from Fig A to Fig B is 3/6  = ½.

The scale factor from Fig B to Fig A is 6/3 = 2

         6 cm                 3 cm
Fig A
Fig B

 

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle is dilated with a scale factor of ½.  Find its

length and width.

6 cm by 10 cm

2 cm by 3 cm

1.5 cm by 2.5 cm

2 cm by  2.5 cm

 

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle is dilated by a scale factor of 2.  Find its

dimensions.

6 cm by 10 cm

2 cm by 3 cm

1.5 cm by 2.5 cm

2 cm by  2.5 cm

If we know one shape's perimeter and the scale factor,

we can find the other shape's perimeter by multiplying

the original perimeter by the scale factor.  If the first

shape has a perimeter of 16 cm and is dilated by a

scale factor of ½, the second shape's perimeter is...

Perimeter = 16

80 cm

5

32 cm

3

8 cm

2.5

80 cm

1.5

If the perimeter is of a shape is 16 cm and is

dilated with scale factor of 2, the perimeter

of the similar shape is...

8 cm

5

32 cm

3

80 cm

3200 cm

a copy

a reduction 

If the scale factor is greater than 100%, 

then the resulting drawing is:

an enlargement

If the scale factor is less than 100%, then the resulting

drawing is:

a reduction

a copy

an enlargement

The perimeter of a triangle is 9 cm.  The

triangle is dilated by a scale factor of 2. 

Find the perimeter of the new triangle.

cm

Figure A is dilated creating Fig B. 

 

What is the scale factor from Fig A to Fig B?

 

What is the perimeter of Fig A?

 

What is the perimeter of Fig B?

Fig A
3
3

Fig B

9
square units
units
9

A rectangle is dilated with a scale factor of 3. 

Which statement correctly describes the perimeter

of the new figure?

 The new perimeter is 1/9 times the original

 The new perimeter is 1/3 times the original

 The new perimeter is 3 times the original

 The new perimeter is 9 times the original

A rectangle is dilated with a scale factor of ⅓. 

Which statement correctly describes the perimeter

of the new figure?

 The new perimeter is 1/9 times the original

 The new perimeter is 1/3 times the original

 The new perimeter is 3 times the original

 The new perimeter is 9 times the original

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