Question

A regular hexagon is dilated by a scale factor of 75 to create a new hexagon. How does the perimeter of the new hexagon compare with the original perimeter?

Answer 1

Let the measure of each side of the hexagon be x units. Therefore the perimeter of the original hexagon = 6x units -----(1) Now, the new hexagon is created by a scale factor of 75. We multiply each side of the hexagon with the scale factor 75. Therefore, the measure of each side of the new hexagon is 75x. The perimeter of the new hexagon = 6 * 75x -----(2) Divide equation (2) by equation (1) 6 * 75x/6x =75 Therefore, when a regular hexagon is dilated by a scale factor, the perimeter of the hexagon is also dilated by the same scale factor.

Answer 2

Let the length of the original hexagon be x:
the perimeter of the hexagon will be:
P=length*number of sides
P=6*x=6x
After the dilation the new length became:
length=scale factor × original length
=75 × x
=75x
thus the new perimeter will be:
6×75x
=450x
hence the new perimeter compared to the old one will be:
450x/6x
=75
the new perimeter is 75 times the old one