Question

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

Answer 1

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.