SOLUTION: A pentagon has an area of 128 square centimeters. A similiar pentagon has an area of 180 square centimeters. What is the ratio of the perimeters of the smaller pentagon to the larg

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Question 312991: A pentagon has an area of 128 square centimeters. A similiar pentagon has an area of 180 square centimeters. What is the ratio of the perimeters of the smaller pentagon to the larger pentagon?

Answer by Alan3354(69443) About Me  (Show Source):
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A pentagon has an area of 128 square centimeters. A similiar pentagon has an area of 180 square centimeters. What is the ratio of the perimeters of the smaller pentagon to the larger pentagon?
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Area is a function of the square of the length of the sides.
Perimeter is a linear function, the 1st power of the lenght of the sides.
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A2/A1 = (P2/P1)^2 = 128/180
(P2/P1)^2 = 128/180 = 32/45
P2%2FP1+=+sqrt%2832%2F45%29
= sqrt%28160%29%2F15
= 4sqrt%2810%29%2F15