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    Question

    The sum of the areas of a rectangle and a square is 432

    cm². The breadth of the rectangle is 6 cm more than each side of the square. If the length of the rectangle is 16 cm, then find the difference between the perimeters of the rectangle and the square.
    A 20 cm Correct Answer Incorrect Answer
    B 32 cm Correct Answer Incorrect Answer
    C 25 cm Correct Answer Incorrect Answer
    D 28 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 + 6) cm Area of the rectangle = 16(x + 6) cm² Area of the square = x² cm² According to the question, 16(x + 6) + x² = 432 Or, x² + 16x + 96 − 432 = 0 Or, x² + 16x − 336 = 0 Or, x² − 12x + 28x − 336 = 0 Or, x(x − 12) + 28(x − 12) = 0 Or, (x − 12)(x + 28) = 0 Or, x = 12, −28 Since length cannot be negative, x = 12 Breadth of rectangle = x + 6 = 18 cm Perimeter of rectangle = 2(16 + 18) = 2 × 34 = 68 cm Each side of the square = x = 12 cm Perimeter of the square = 4 × 12 = 48 cm Required difference = 68 − 48 = 20 cm

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