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    Question

    The perimeter of a rectangle of length 2(x + 5) cm and

    breadth 2(x + 2) cm is double the perimeter of a square of area 324 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 = 324 cm²   Side of square = √324 = 18 cm   Perimeter of square = 18 × 4 = 72 cm   So, perimeter of rectangle = 2 × 72 = 144 cm   ⇒ 2(2(x + 5) + 2(x + 2)) = 144   ⇒ 4x + 14 = 72   ⇒ 4x = 58   ⇒ x = 14.5   So, length of rectangle = 2(14.5 + 5) = 39 cm   And, breadth of rectangle = 2(14.5 + 2) = 33 cm   Therefore, area of rectangle = 39 × 33 = 1287 cm²

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