# If the star has an outside perimeter of 50, and the pentagon has a perimeter of 30, what is AB + BC + CD + DE + EA = ?

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If the star has an outside perimeter of 50, and the pentagon has a perimeter of 30, what is AB + BC + CD + DE + EA = ??

posted Apr 23, 2016

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Outside perimeter = AH+DH+DG+BG+BF+EF+EJ+CJ+CI+AI = 50

Pentagon perimeter = HG+GH+FJ+JI+IH = 30

(AH+DH+DG+BG+BF+EF+EJ+CJ+CI+AI) + (HG+GH+FJ+JI+IH) = 50 + 30
Rearranging them,
(AH+HG+BG)+(BF+FJ+CJ)+(CI+IH+DH)+(DG+GF+EF)+(EJ+AI+JI) = 80
that is AB+BC+CD+DE+EA=80

AB + BC + CD + DE + EA =
(AH+HG+GB)+(BF+FJ+JC)+(CI+IH+HD)+(DG+GF+FE)+(EJ+JI+IA)=

(AH+HC+CG+GB+BF+FE+EJ+JC+CI+IA)+(HG+GF+FJ+JI+IH)=
outside perimeter of star + perimeter of pentagon=
50+30= 80
the required ans is =80.

Let us take one triangle
triangle AHI, AH = AI
All green shaded triangles are equal and taking into account that the external perimeter is 50
Length of AH = 50 / 10 = 5
Inside pentagon
Length of HG = 30/5 = 6
Now, Length of AH+HG+GB = 5 + 6 +5 = 16
The total perimeter of AB+BC+CD+DE+EA wil be 16 * 5 = 80

answer Apr 27, 2016 by anonymous

Outside star perimeter = 50
Outside star sides =5*2=10
Length of one side of outside star=50/10=5

Pentagon perimeter 30
Pentagon side = 30/5=6

Length of one side of star = 5+6+5=16
Length of 5 sides = 5*16= 80

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