Question

A square whose side is 2m has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon in meters is

Answer 1

Let ABCd is a square and AB = BC = CD= DA = 2 m Again, we form a rectangular octagon by cutting all four corners. Let EF = FG = GH = HI = IJ = JK = KL = LE = x Now, by symmetry, we get AE = Al = BG = BF = Ch = CI = DJ = Dk = a In triangle ALE, apply Pythagorus theorem, AL2= AE2+ LE2 => x2= a2+ a2 => x2= 2a2 => x = a√2 => a = x/√2 ....................1 Again, AB = AE + EF + FB. => 2 = a + x + a => 2 = 2a + x => 2 = 2x/√2 + x => √2x + x = 2 => (√2 + 1)x = 2 => x = 2/(√2 + 1) So, the side of an octagon is 2/(√2 + 1) m