If a figure is dilated by a factor of 6, the perimeter of the figure will change by a factor of ___.

Question

Mathematics

Todd

15 January, 09:54

If a figure is dilated by a factor of 6, the perimeter of the figure will change by a factor of ___.

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Erik Lucas · Answer 1

If a figure is dilated by a factor of 6, the perimeter of the figure will change by a factor of 6.

Step-by-step explanation:

The objects that have the same shape are known as similar figures. Since they are similar in shape it doesn't necessary for those objects to have the same size.

Dilation is the process that enlarges or shrinks the size of an object to its similar figure without changing its size. The Dilation is based on a factor that makes the object to enlarge or shrink.

Since its size has changed so as the perimeter will be changed for both of the figures. The perimeter of an object remains same as the scale factor used to dilate the object.

Consider a square with its side as 2 cm initially and dilated with factor 3.

Perimeter of the square = 4 a. where a is the side.

Then the perimeter of the square will be 8 cm initially.

After dilation the side of the square will be changed as 6.

Then the perimeter will change as 24 cm.

Thus the perimeter of the square initially has increased 3 times after dilation.