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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

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

Grade:12

2 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

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

aditya jha
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)

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