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    Question

    Length and breadth of a rectangle are 8 cm and 6 cm respectively. The rectangle is cut on its four vertices such that the resulting figure is a regular octagon. What is the side (in cm) of the octagon?

    A 3(√11) – 7 Correct Answer Incorrect Answer
    B 5(√13) – 8 Correct Answer Incorrect Answer
    C 4(√7) – 11 Correct Answer Incorrect Answer
    D 6(√11) – 9 Correct Answer Incorrect Answer

    Solution

    Let the side of octagon is x Apply PGT x2 = (6 – x / 2)2 + (8 – x / 2)2 x2 = (36 + x2 – 12x + 64 + x2 – 16x / 4) 4x2 = 100 + 2x2 – 28x = 2x2 + 28x + 100 = 0 = x2 + 14x + 50 = 0 X = 3√11 – 7 cm

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