Question #158210

Given two regu

lar polygons of the same number of sides. If the area of the first is

3 times the area of the second, find the ratio of (a) their perimeters, and (b) their

apothems.



1
Expert's answer
2021-01-28T05:21:13-0500

If two regular polygons of the same number of sides are given then such polygons are

similar


k=side1sie2=perimeter1perimeter2=apothem1apothem2k=\dfrac{side_1}{sie_2}=\dfrac{perimeter_1}{perimeter_2}=\dfrac{apothem_1}{apothem_2}

=Area1Area2=\sqrt{\dfrac{Area_1}{Area_2}}

Given Area1Area2=3\dfrac{Area_1}{Area_2}=3

(a)

perimeter1perimeter2=3\dfrac{perimeter_1}{perimeter_2}=\sqrt{3}

(b)


apothem1apothem2=3\dfrac{apothem_1}{apothem_2}=\sqrt{3}



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