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Answer :
Answer: 35 inches
Each side of the pentagon is multiplied by 5/3 to get the length of each new side, so the perimeter is multiplied by 5/3 to get the new perimeter.
New perimeter = (scale factor)*(old perimeter)
New perimeter = (5/3)*(old perimeter)
New Perimeter = (5/3)*(21)
New Perimeter = (5/3)*(21/1)
New Perimeter = (5*21)/(3*1)
New Perimeter = 105/3
New Perimeter = 35 inches
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Final answer:
To find the perimeter of the new pentagon after dilation by a scale factor of 5/3, you multiply the side length of the original pentagon (4.2 inches) by the scale factor to get the new side length (7 inches), then multiply by the number of sides (5) to get the new perimeter (35 inches).
Explanation:
To find the perimeter of the dilated pentagon, we can use the information that a regular pentagon with a perimeter of 21 inches is dilated by a scale factor of 5/3.
First, we find the length of one side of the original pentagon by dividing the total perimeter by the number of sides:
- Perimeter of original pentagon / Number of sides = Side length
- 21 inches / 5 = 4.2 inches
Next, we multiply the side length by the scale factor to find the new side length:
- New side length = Original side length × Scale factor
- New side length = 4.2 inches × (5/3)
- New side length = 7 inches
Finally, to find the perimeter of the new pentagon, we multiply the new side length by the number of sides:
- Perimeter of new pentagon = New side length × Number of sides
- Perimeter of new pentagon = 7 inches × 5
- Perimeter of new pentagon = 35 inches
Therefore, the perimeter of the new pentagon is 35 inches.
