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Question

A landscaper is designing a rectangular garden. The length of the garden is to be 5 feet longer than the width. If the area of the garden will be 104 square feet, what will be the length, in feet, of the garden?

The correct answer is: 13


    The length of garden in feet will be 13 feets.
    For solving this question,
    Let x represent the width of the rectangular garden, in feet.
    Since we are given length of the garden will be 5 feet longer than the width of the garden,
    The length of the garden will be x + 5 feet.
    Thus the area of the garden will be
    Area = (length)(width)
    Area = x(x + 5).
    It is also given that the area of the garden will be 104 square feet.
    Therefore, x(x + 5) = 104,
    Further solving we get ,
    x2 + 5x −104 = 0.
    The quadratic formula can be used or the equation above can be factorised as follows;
    (w + 13)(w − 8) = 0.
    Therefore, equating both the brackets with zero we get
    w = 8 and w = −13
    Because width cannot be negative, the width of the garden must be 8 feet.
    This means the length of the garden will be
    8 + 5 = 13 feet.
    Therefore the length of the garden is 13 feets.
    Note:- There are different ways of solving quadratic equations.
    • Solving quadratic equations by factoring
    • Solving quadratic equations by completing the square
    • Solving quadratic equations by graphing
    • Solving quadratic equations by quadratic formula
    But most popular method is solving quadratic equations by factoring.

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