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    Question

    The total area of a square and a rectangle is 306 cm².

    The breadth of the rectangle is 6 cm more than the length of each side of the square. If the length of the rectangle is 18 cm, then what is the difference between the perimeters of the rectangle and the square?
    A 20 cm Correct Answer Incorrect Answer
    B 18 cm Correct Answer Incorrect Answer
    C 30 cm Correct Answer Incorrect Answer
    D 45 cm Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    18(x + 6) + x² = 306 Or, x² + 18x + 108 – 306 = 0 Or, x² + 18x – 198 = 0 Or, x² – 9x + 27x – 198 = 0 Or, x(x – 9) + 22(x – 9) = 0 Or, (x – 9)(x + 22) = 0 Or, x = 9, -22 Since the side cannot be negative, x = 9 Breadth of rectangle = x + 6 = 15 cm Perimeter of rectangle = 2(15 + 18) = 2 × 33 = 66 cm Each side of the square = x = 9 cm Perimeter of square = 4 × 9 = 36 cm Required difference = 66 - 36 = 30 cm

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