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      Question

      The perimeter of a rectangle of length 2(x + 4) cm and

      breadth 2(x + 3) cm is double the perimeter of a square of area 484 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 = 484 cm²   Side of square = √484 = 22 cm   Perimeter of square = 22 × 4 = 88 cm   So, perimeter of rectangle = 2 × 88 = 176 cm   ⇒ 2(2(x + 4) + 2(x + 3)) = 176   ⇒ 4x + 14 = 88   ⇒ 4x = 74   ⇒ x = 18.5   So, length of rectangle = 2(18.5 + 4) = 45 cm   And, breadth of rectangle = 2(18.5 + 3) = 43 cm   Therefore, area of rectangle = 45 × 43 = 1935 cm²

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