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Applications of Scale Factor

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Caroline Chaneski

on 2 January 2014

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Transcript of Applications of Scale Factor

Scale Factor - The ratio of the lengths of two corresponding sides of two similar polygons.

Math Definition of Scale Factor
Applications of Scale Factor
Perimeter is the sum of all the sides of a shape. To determine the perimeter of a figure add the lengths of all the sides. Since perimeter is based on addition, let’s look at how scale factor affects addition.
A rectangle that measures 5 cm by 3 cm has a perimeter equal to the sum of 5 + 3 + 5 + 3. Therefore, the perimeter of a 5 cm by 3 cm rectangle is 16 cm.
P = l + w + l + w or P = 2l + 2w
Perimeter of the original figure is 16 cm
Suppose the scale factor is 2, this means that we multiply each side of the original figure by 2. The length of 5 cm multiplied by 2 is now 10 cm. The width of 3 cm multiplied by 2 is now 6 cm. The sum of 10 + 6 + 10 + 6 is 32 cm. By applying a scale factor of 2 to the original figure, the result is a perimeter that is twice as large as or two times larger than the original rectangle.
P = 2(10) + 2(6)
P = 20 + 12
Perimeter of the new figure is 32 cm
Notice that 16 cm times 2 equals 32 cm.

How does applying a Scale Factor affect perimeter and circumference: http://eigthgrademathmocity.wikispaces.com/Effect+on+Area+and+Perimeter+when+dimensions+are+changed+proportionally#perimeter
Perimeter and Circumference
Example 1: Enlargement
In order to determine the scale factor used to transform one figure into a similar figure, divide the length of one side of the new image by the corresponding side of the original figure.
The formula is: New
Original
A'C' 15 3
AC 5 1
|
|
| 4 cm
|
|
|---------- 6 cm --------|
|---------- 5 cm ---------|
|
|
|
|
|
| 12 cm
|
|
|
|
|
|--------------------- 18 cm -------------------|
|--------------------- 15 cm -------------------|

A





B M C
A'







B' M' C'
Original
Image
or
New Figure
____ : __ = __ =
3
B'C' 18 3
BC 6 1
____ : __ = __ =
3
∆ABC ~ ∆A’B’C’
|----------9 cm--------|
A'M' 12 3
AM 4 1
____ : __ = __ =
3
How does the scale factor affect perimeter?
Applying a
scale factor
to a figure dilates the figure.
A
scale factor
that is
greater than 1
results in an
enlargement.
Enlargement: SF > 1

Applying a
scale factor greater than 0 and less than 1
results in a
reduction
. Reduction: 0<SF<1

Applying a
scale factor equal to 1
results in a duplicate copy of the original figure or
no change
.
Example 2: Enlargement
A rectangle that measures 5 cm by 3 cm has a perimeter equal to the sum of 5 + 3 + 5 + 3. Therefore, the perimeter of a 5 cm by 3 cm rectangle is 16 cm.
P = l + w + l + w or P = 2l + 2w
Perimeter of the original figure is 16 cm
Suppose the scale factor is 3, this means that we multiply each side of the original figure by 3. The length of 5 cm multiplied by 3 is now 15 cm. The width of 3 cm multiplied by 3 is now 6 cm. The sum of 15 + 9 + 15 + 9 is 48 cm. By applying a scale factor of 3 to the original figure, the result is a perimeter that is triple the size or three times larger than the original rectangle.
P = 2(15) + 2(9)
P = 30 + 18
Perimeter of the new figure is 48 cm
Notice that 16 cm times 3 equals 48 cm.

Example 3: Enlargement
A rectangle that measures 5 cm by 3 cm has a perimeter equal to the sum of 5 + 3 + 5 + 3. Therefore, the perimeter of a 5 cm by 3 cm rectangle is 16 cm.
P = l + w + l + w or P = 2l + 2w
Perimeter of the original figure is 16 cm
Suppose the scale factor is 5, this means that we multiply each side of the original figure by 3. The length of 5 cm multiplied by 3 is now 15 cm. The width of 3 cm multiplied by 3 is now 6 cm. The sum of 25 + 15 + 25 + 15 is 80 cm. By applying a scale factor of 3 to the original figure, the result is a perimeter that is triple the size or three times larger than the original rectangle.
P = 2(25) + 2(15)
P = 50 + 30
Perimeter of the new figure is 80 cm
Notice that 16 cm times 5 equals 80 cm.

A rectangle that measures 10 cm by 6 cm has a perimeter equal to the sum of 10 + 6 + 10 + 6. Therefore, the perimeter of a 10 cm by 6 cm rectangle is 32 cm.
P = l + w + l + w or P = 2l + 2w
Perimeter of the original figure is 32 cm

Suppose the scale factor is 0.5, this means that we multiply each side of the original figure by 0.5. The length of 10 cm multiplied by 0.5 is now 5 cm. The width of 6 cm multiplied by 0.5 is now 3 cm. The sum of 5 + 3 + 5 + 3 is 16 cm. By applying a scale factor of 0.5 to the original figure, the result is a perimeter that is half the size of the original rectangle.
P = 2(5) + 2(3) = 10 + 6
Perimeter of the new figure is 16 cm
Notice that half of 32 cm is 16 cm.

Example 1:Reduction
A rectangle that measures 20 cm by 12 cm has a perimeter equal to the sum of 20 + 12 + 20 + 12. Therefore, the perimeter of a 20 cm by 12 cm rectangle is 64 cm.
P = l + w + l + w or P = 2l + 2w
Perimeter of the original figure is 64 cm

Suppose the scale factor is 0.25, this means that we multiply each side of the original figure by 0.25. The length of 10 cm multiplied by 0.25 is now 5 cm. The width of 6 cm multiplied by 0.25 is now 3 cm. The sum of 5 + 3 + 5 + 3 is 16 cm. By applying a scale factor of 0.25 to the original figure, the result is a perimeter that is a quarter or one fourth the size of the original rectangle.
P = 2(5) + 2(3) = 10 + 6
Perimeter of the new figure is 16 cm
Notice that one fourth of 64 cm is 16 cm.

Example 2:Reduction
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