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Two polygons are similar. The perimeter of the larger polygon is 85 meters and the ratio of the corresponding side lengths is [tex]\frac{2}{5}[/tex]. Find the perimeter of the other polygon.

Respuesta :

LammettHash

Suppose the polygons have 3 sides, [tex]s_1,s_2,s_3[/tex]. In the smaller polygon, the corresponding sides would have lengths [tex]\dfrac25s_1,\dfrac25s_2,\dfrac25s_3[/tex].

So if the perimeter of the larger polygon is

[tex]s_1+s_2+s_3=85[/tex]

then the perimeter of the smaller polygon would be

[tex]\dfrac25(s_1+s_2+s_3)=\dfrac25\cdot85[/tex]

so its perimeter would be 34 meters.

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