A regular pentagon with a perimeter of 21 inches is dilated by a scale factor of #5/3# to create a new pentagon. What is the perimeter of the new pentagon?

1 Answer
Solace M.
Sep 20, 2017

35 inches

Explanation:

This assumes the dilation happens in the centre of the pentagon. A regular pentagon with a perimeter of 21 inches has side lengths equal to #21/5=4.2# inches. The dilation factor is #5/3#, therefore
#4.2*5/3=7# inches being the new side length. Since this is a regular pentagon, we multiply the side length by 5 to get
#7*5=35# inches is the new perimeter.

Alternatively, you could just multiply the perimeter by the dilation, so
#21*5/3#
#=105/3#
#=35# inches as the new perimeter.

I hope I helped!

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