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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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

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