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    Question

    A rectangular garden has a length of 100 cm. The ratio of the width of the garden to the side of a square flower bed is 5: 8. If the ratio of the perimeter of the garden to the perimeter of the flower bed is 5:12, what is the area of the garden?

    A 28,000 cm² Correct Answer Incorrect Answer
    B 30,000 cm² Correct Answer Incorrect Answer
    C 32,000 cm² Correct Answer Incorrect Answer
    D 35,000 cm² Correct Answer Incorrect Answer
    E 36,000 cm² Correct Answer Incorrect Answer

    Solution

    Let the width of the garden be 5x cm. Let the side of the square flower bed be 8x cm. Perimeter of the garden = 2 * (length + width) = 2 * (100 + 5x) Perimeter of the flower bed = 4 * side = 4 * 8x = 32x 5: 12 = (2 * (100 + 5x)): (32x) Simplifying, we get: 5 * 32x = 12 * 2 * (100 + 5x) 160x = 2400 + 120x 40x = 2400 x = 60 Width of the garden = 5x = 5 * 60 = 300 cm Area of the garden = length * width = 100 *  300 = 30,000 cm² Ans. B

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