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 $\frac{a}{b}$, the area of the figure is  dilated by a scale factor of $\frac{a^{2}}{b^{2}}$

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 $\frac{1}{2}$ to produce a new rectangle.

So we will find the square of scale factor = $(\frac{1}{2})^{2}=\frac{1}{4}$

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

= $80*\frac{1}{4}=20$

Hence, area becomes 20 square cm.