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    Question

    The perimeter of a rectangle of length 2(x + 6) cm and

    breadth 2(x + 5) cm is double the perimeter of a square of area 361 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

    Solution

      Area of square = 361 cm²   Side of square = √361 = 19 cm   Perimeter of square = 19 × 4 = 76 cm   So, perimeter of rectangle = 2 × 76 = 152 cm   ⇒ 2(2(x + 6) + 2(x + 5)) = 152   ⇒ 4x + 22 = 76   ⇒ 4x = 54   ⇒ x = 13.5   So, length of rectangle = 2(13.5 + 6) = 39 cm   And, breadth of rectangle = 2(13.5 + 5) = 37 cm   Therefore, area of rectangle = 39 × 37 = 1443 cm2

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