document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #278331 by robertb(5830) $\"\"$ $\"About$

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Let x = side of the regular octagon. By symmetry, each figure cut from the corners must be an isosceles right (45-45-90) triangle,
\n" ); document.write( "and all four of them must be congruent. Then the leg of each isosceles triangle must have measure $\"x%2Fsqrt%282%29\"$ .
\n" ); document.write( "Then we must have $\"x%2Fsqrt%282%29+%2B+x+%2B+x%2Fsqrt%282%29+=+2\"$ , or
\n" ); document.write( " $\"sqrt%282%29x+%2B+x+=+2\"$ after simplification, or
\n" ); document.write( " $\"%281%2Bsqrt%282%29%29x+=+2\"$ , or
\n" ); document.write( " $\"x+=+2%2F%281%2Bsqrt%282%29%29\"$ meter. \n" ); document.write( "

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