Mathematics: The ratio of the areas of two similar polygons is 81: 64. if the perimeter of the first polygon is 32 cm, what is the perimeter of the second polygon? round to the nearest tenth

The ratio of the areas of two similar polygons

aricketts3901

15.03.2022

In two similar polygons, the ratio of their areas is the square of the ratio of their sides. If the sides of any polygon are a and b then :

Ratio of area = $a^{2} :b^{2}$

Given ratio of area =81:64

Or 81:64= $a^{2} :b^{2}$

Taking root of both sides

9:8=a:b

The ratio of perimeter of any two similar polygon is equal to the ratio of sides.

Ratio of perimeter = a:b

Perimeter of first polygon is 32 cm.

Let the perimeter of second polygon be x.

32:x=a:b

Or, 32:x=9:8

$\frac{32}{x} =\frac{9}{8}$

Cross multiplying

9x= (32)(8)

9x=256

Dividing both sides by 9

x=28.4.

The perimeter of second polygon is 28.4cm.

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