Given:
Perimeter of a regular pentagon = 10 cm
The pentagon is dilated by a scale factor = [tex]\dfrac{3}{2}[/tex].
To find:
The perimeter of the new pentagon.
Solution:
If a figure is dilated by a scale factor k, then
Perimeter of new figure = k × perimeter of original figure
The scale factor is [tex]\dfrac{3}{2}[/tex] and the perimeter of a regular pentagon is 10 cm. So, the perimeter of a new pentagon is:
[tex]\text{Perimeter of new pentagon}=\dfrac{3}{2}\times 10[/tex]
[tex]\text{Perimeter of new pentagon}=3\times 5[/tex]
[tex]\text{Perimeter of new pentagon}=15[/tex]
Therefore, the perimeter of the new pentagon is 15 cm.
