# math

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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

• math -

We would need to cut out four corners to make a regular octagon (all 8 sides of equal length) from the square.

Each corner cut out will be an isosceles right-angled triangle with short sides of length x, and hypotenuse (√2)x.

Since the hypotenuse forms one side of the octagon, all eight sides are of length (√2)x.

The length of one side of the square is therefore:

L = x + (√2)x + x = 2 m

Solving for x:
(1 + √2 + 1)x = 2
x = 2/(2+√2)

and the length of each side of the octagon is
(√2)x
= (2√2)/(2+√2)
= 0.8284 m (approx.)

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