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    Question

    The sum of the areas of a rectangle and a square is 161

    cm². The breadth of the rectangle is 1 cm more than each side of the square. If the length of the rectangle is 14 cm, then find the difference between the perimeters of the rectangle and the square.
    A 20 cm Correct Answer Incorrect Answer
    B 12 cm Correct Answer Incorrect Answer
    C 16 cm Correct Answer Incorrect Answer
    D 18 cm Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, Let the length of each side of the square be ‘x’ cm Therefore, breadth of the rectangle = (x + 1) cm Area of the rectangle = 14(x + 1) cm² Area of the square = x² cm² According to the question, 14(x + 1) + x² = 161 Or, x² + 14x + 14 − 161 = 0 Or, x² + 14x − 147 = 0 Or, x² − 7x + 21x − 147 = 0 Or, x(x − 7) + 21(x − 7) = 0 Or, (x − 7)(x + 21) = 0 Or, x = 7, −21 Since length cannot be negative, x = 7 Breadth of rectangle = x + 1 = 8 cm Perimeter of rectangle = 2(14 + 8) = 2 × 22 = 44 cm Each side of the square = x = 7 cm Perimeter of the square = 4 × 7 = 28 cm Required difference = 44 − 28 = 16 cm

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