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elizabethann509 Group Title

How do I solve this? The ratio of the areas of two similar polygons is 49:16. If the perimeter of the first polygon is 22 cm, what is the perimeter of the second polygon?

  • 2 years ago
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  1. happytreefriend7 Group Title
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    If these are regular polygons, then the question involves some manipulation of the equation: \[Area = (s^{2}*N)/(4 \tan (180/N))\] where s = the length of a side, and N = the number of sides. Since we're assuming the polygon is regular, the perimeter can be represented by the following equation: p = sN. Set up a ratio of areas (e.g Area1/ Area2 = 49/16) and the denominators cancel. You're left with \[Area_1/Area_2 = ( p^2_1N )(p^2_2N)\]. The "N"s cancel, and you get an equation relating area and perimeter for *regular* polygons. I hope you can take it from there.

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