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Let the number of sides be x and use the diagonal formula:-

If: 0.5*(x^2 -3x) = 90 then x^2 -3x = 90*2

If: x^2 -3x = 180 then x^2 -3x -180 = 0

Using the quadratic equation formula gives a positive value of 15 for x

Therefore perimeter of the polygon: 15*4 = 60 cm

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βˆ™ 2016-06-17 11:41:48
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Q: What is the perimeter of a regular polygon when each side is 4 cm and has 90 diagonals showing work?
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