SOLUTION: There is a square with each of it’s side is of 2m. An octagonal is cut-of from this square by cutting it’s edge such that the octagonal has all it’s sides equal. Find out the lengt

Algebra ->  Length-and-distance -> SOLUTION: There is a square with each of it’s side is of 2m. An octagonal is cut-of from this square by cutting it’s edge such that the octagonal has all it’s sides equal. Find out the lengt      Log On


   

Question 392141: There is a square with each of it’s side is of 2m. An octagonal is cut-of from this square by cutting it’s edge such that the octagonal has all it’s sides equal. Find out the length of each side of the octagonal?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = side of the regular octagon. By symmetry, each figure cut from the corners must be an isosceles right (45-45-90) triangle,
and all four of them must be congruent. Then the leg of each isosceles triangle must have measure x%2Fsqrt%282%29.
Then we must have x%2Fsqrt%282%29+%2B+x+%2B+x%2Fsqrt%282%29+=+2, or
sqrt%282%29x+%2B+x+=+2 after simplification, or
%281%2Bsqrt%282%29%29x+=+2, or
x+=+2%2F%281%2Bsqrt%282%29%29 meter.