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# a square whose side is 2m,has its corndrs cut away so as to form an octagon with all sides equal.then the length of each side of the octagon,in metres is

Chetan Mandayam Nayakar
312 Points
10 years ago

let side of octagon=a, then a+2(a/√2) =2, a=2/(√2 +1) metres

11 Points
3 years ago
ABCD is square and PQRSTUVW is octagon with equal sides constructed with in the square.

In order to have octagon with equal sides, we should have AP=QB=BR=SC=CT=….
Let AP=AW=x;
Let PQ = y; as all sides of octagon are equal, QR=RS=ST=TU=UV=VW=WP=y;
As the length of side of square is 2,
2x+y = 2         ------(1)
Applying Pythagoras to the right triangle APW, y2 = x2+x2 = 2x2
=>  y= x√2      ------(2)
Solving (1) and (2):
2x+x√2 = 2 => x = 2/(2+√2) = √2/(√2+1)
=>  y = x√2 = 2/(√2+1)