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    Question

    The combined area of a rectangle

    and a square is 244 cm². The breadth of the rectangle is 4 cm longer than the side of the square. If the rectangle’s length is 15 cm, find the difference between the perimeters of the rectangle and the square.
    A 18 cm Correct Answer Incorrect Answer
    B 22 cm Correct Answer Incorrect Answer
    C 32 cm Correct Answer Incorrect Answer
    D 42 cm Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let the length of each side of the square be ‘x’ cm Therefore, breadth of the rectangle = (x + 4) Area of the rectangle = 15(x + 4) cm2 Area of the square = x2 cm2 According to the question, 15(x + 4) + x2 = 244 Or, x2 + 15x + 60 – 244 = 0 Or, x2 + 15x – 184 = 0 Or, x2 – 8x + 23x – 184 = 0 Or, x(x – 8) + 23(x – 8) = 0 Or, (x – 8)(x + 23) = 0 Or, x = 8, -23 Since, the length cannot be negative therefore, x = 8 Breadth of rectangle = x + 4 = 12 cm Perimeter of rectangle = 2(12 + 15) = 2 × 27 = 54 cm Each side of the square = x = 8 cm Perimeter of the square = 4 × 8 = 32 cm Required difference = 54 - 32 = 22 cm

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