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nikdorinn [45]
3 years ago
14

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

Mathematics
1 answer:
natta225 [31]3 years ago
4 0

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.

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