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    Question

    The perimeter of a rectangle of length 2(x + 2) cm and

    breadth 2(x + 4) cm is double the perimeter of a square of area 256 cm². Find the area of the rectangle.
    A 1020 cm² Correct Answer Incorrect Answer
    B 1287 cm² Correct Answer Incorrect Answer
    C 1935 cm² Correct Answer Incorrect Answer
    D 1443 cm² Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Area of square = 256 cm²   Side of square = √256 = 16 cm   Perimeter of square = 16 × 4 = 64 cm   So, perimeter of rectangle = 2 × 64 = 128 cm   ⇒ 2(2(x + 2) + 2(x + 4)) = 128   ⇒ 4x + 12 = 64   ⇒ 4x = 52   ⇒ x = 13   So, length of rectangle = 2(13 + 2) = 30 cm   And, breadth of rectangle = 2(13 + 4) = 34 cm   Therefore, area of rectangle = 30 × 34 = 1020 cm²

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