As a regular pentagon is dilated by a scale factor of 3 to create a new pentagon, which statement is true?

A. The perimeter of the new pentagon is \(\frac{9}{4}\) the perimeter of the original.
B. The perimeter of the new pentagon is \(\frac{9}{2}\) the perimeter of the original.
C. The perimeter of the new pentagon is \(\frac{15}{2}\) the perimeter of the original.
D. The perimeter of the new pentagon is \(\frac{3}{2}\) the perimeter of the original.

When a shape is dilated by a scale factor, all lengths within the shape are multiplied by that factor. So, when the regular pentagon is dilated by a scale factor of 3, the perimeter of the new pentagon is 3 times the original. The correct answer is that the perimeter of the new pentagon is 9/2 the perimeter of the original.

Explanation:

In the subject of Mathematics, particularly with shapes and scaling, when a shape is dilated by a scale factor, all lengths within the shape are multiplied by that factor. So, when your regular pentagon is dilated by a scale factor of 3, this means that each side of the pentagon is multiplied by 3. As the pentagon has 5 sides, the total perimeter will be multiplied by 3 as well.

Therefore, the perimeter of the new pentagon is 3 times the perimeter of the original pentagon. This eliminates options F, H, and J, and we find that the correct answer is:

G. The perimeter of the new pentagon is 9/2 the perimeter of the original.

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