A regular pentagon is dilated by a scale factor of 1.5 to create a new pentagon. Which of the following statements is true? The perimeter of the new pentagon is 2.25 the perimeter of the original pentagon.
The perimeter of the new pentagon is 4.5 the perimeter of the original pentagon.
The perimeter of the new pentagon is 7.5 the perimeter of the original pentagon.
The perimeter of the new pentagon is 1.5 the perimeter of the original pentagon.
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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58