Question

    The perimeter of a square and a rectangle is in the

    ratio of 16:15. The square has an area of 256 cm², and the length of the rectangle is 12.5% greater than the side length of the square. Determine the area of the rectangle.
    A 200 sq cm Correct Answer Incorrect Answer
    B 216 sq cm Correct Answer Incorrect Answer
    C 192 sq cm Correct Answer Incorrect Answer
    D 180 sq cm Correct Answer Incorrect Answer
    E 240 sq cm Correct Answer Incorrect Answer

    Solution

    Given, area of the square = 256 cm2 So, the side of the square = √256 = 16 cm Or, the perimeter of the square = 4 X 16 = 64 cm So, the perimeter of the rectangle = (64/16) X 15 = 60 cm Length of the rectangle = 16 X (9/8) = 18 cm Let the breadth of the rectangle be 'y' cm So, perimeter of the rectangle = 2 X (length + breadth) 60 = 2 X (18 + y) Or, 30 = 18 + y Or, 'y' = 12 Therefore, area of the rectangle = 18 X 12 = 216 cm2

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