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Suppose a regular pentagon with a perimeter of 34 inches was dilated by a scale factor of 0.25. Fill in the blanks in the following sentences. Do not round your answers.

The pentagon’s side length before the dilation was in.
The new side length after the dilation was in., and its perimeter after the dilation was in.

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boffeemadrid

Answer:

[tex]6.8\ \text{in}[/tex]

[tex]8.5\ \text{in}[/tex]

[tex]1.7\ \text{in}[/tex]

Step-by-step explanation:

Perimeter of the pendulum = 34 inches

Scale factor = 0.25

x = Length of side of pentagon

[tex]5x=34\\\Rightarrow x=\dfrac{34}{5}\\\Rightarrow x=6.8\ \text{in}[/tex]

The pentagon’s side length before the dilation was [tex]6.8\ \text{in}[/tex].

New perimeter of the pentagon

[tex]34\times 0.25=8.5\ \text{in}[/tex]

New perimeter of the pentagon is [tex]8.5\ \text{in}[/tex].

[tex]5x=8.5\\\Rightarrow x=\dfrac{8.5}{5}\\\Rightarrow x=1.7\ \text{in}[/tex]

The new side length of the perimeter is [tex]1.7\ \text{in}[/tex].

akposevictor

The Pentagon's side length before dilation = 6.8 inches

New side length of pentagon = 1.7 inches.

Perimeter of Pentagon after dilation: 8.5 inches

Recall:

  • Scale factor of dilation = dimension of new shape / dimension of original shape
  • Perimeter of pentagon = 5s. Where s = side length

Given:

Perimeter of pentagon = 34 inches

Scale factor of dilation = 0.25

Pentagon's side length before dilation:

Perimeter = 5s

  • Substitute

34 = 5s

  • Divide both sides by 5

34/5 = s

6.8 = s

  • Side length of pentagon before dilation = 6.8 inches

New side length of Pentagon after dilation:

Scale factor = new side length/original side length

  • Substitute

0.25 = new side length/6.8

  • Multiply both sides by 6.8

0.25 × 6.8 = new side length

New side length of pentagon = 1.7 inches.

Perimeter of Pentagon after dilation:

Perimeter of Pentagon = 5s

  • Substitute

Perimeter = 5(1.7)

Perimeter = 8.5 inches

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