A square whose side is 2 metres has itscorners cut away so as to form

1.	A square whose side is 2 metres has itscorners cut away so as to form anoctagon with all sides equal. Then, thelength of each side of the octagon inmetres is
Answer» 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)

A square whose side is 2 metres has itscorners cut away so as to form anoctagon with all sides equal. Then, thelength of each side of the octagon inmetres is

Answer»

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)