A regular octagan is formed by cutting off each corner of a square of side 8 cm. The length of each side is ____________.
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LET THE SIDE OF THE OCTAGON FORMED FROM THE SQUARE BE x cm
portion cut forms a right angled triangle. Length of each side of the triangular portion of the paper cut from the corners of the paper = (8 - x)/2
⇒ x2 = [(8 - x)2 / 4] + [(8 - x)2 / 4]
⇒ x2 = [(8 - x)2 / 4] + [(8 - x)2 / 4]
⇒ x2 = 2 [(8 - x)2 / 4]
⇒ x2 = [(8 - x)2 / 2]
⇒ x2 + 16x - 64 = 0
⇒ x = -8 + 8√2, -8 - 8√2
⇒ x = 3.31 or -19.31
Side of the octagon formed from a square of 8 cm = 3.31 cm
portion cut forms a right angled triangle. Length of each side of the triangular portion of the paper cut from the corners of the paper = (8 - x)/2
⇒ x2 = [(8 - x)2 / 4] + [(8 - x)2 / 4]
⇒ x2 = [(8 - x)2 / 4] + [(8 - x)2 / 4]
⇒ x2 = 2 [(8 - x)2 / 4]
⇒ x2 = [(8 - x)2 / 2]
⇒ x2 + 16x - 64 = 0
⇒ x = -8 + 8√2, -8 - 8√2
⇒ x = 3.31 or -19.31
Side of the octagon formed from a square of 8 cm = 3.31 cm
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