Question

When a rectangle is dilated, how do the perimeter and area of the rectangle change?

Answer 1

A transformation of a figure in which all of the dimensions of the figure are multiplied by the same scale factor is called a dilation.

Effect of Dilation on Perimeter

Whenever a figure is dilated by a scale factor, the perimeter of the figure changes according to the same scale factor.

Effect of Dilation on Area

When a figure is dilated by a scale factor of
`(a)/(b)`, the area of the figure is dilated by a scale factor of
`(a^(2))/(b^(2))`

Example-

Lets imagine a rectangle with length 10 cm and width 8 cm

So area becomes = 10*8 = 80 square cm

Lets suppose the rectangle is reduced by a scale factor of
`(1)/(2)` to produce a new rectangle.

So we will find the square of scale factor =
`((1)/(2))^(2)=(1)/(4)`

Now to find the area of the new rectangle(dilated one) we will multiply the area of the original rectangle by 1/4

=
`80*(1)/(4)=20`

Hence, area becomes 20 square cm.