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Math Help - Quadratic Equation Word Problem

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    Quadratic Equation Word Problem

    Translate the following into a quadratic equation, and solve it:
    The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its dimensions?
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    Quote Originally Posted by MathGeek06 View Post
    Translate the following into a quadratic equation, and solve it:
    The length of a rectangular garden is three times its width; if the area of the garden is 75 square meters, what are its dimensions?
    You are supposed to know that the area of a rectangle is calculated by:

    A=l \cdot w~,~w,l \geq 0

    You know that l = 3w . Plug in this term instead of l into the formula and you get:

    a = 3w \cdot w = 75 . Therefore:

    3w^2 = 75~\iff~w^2 = 25~\iff~ w = 5

    So the dimensions of the rectangle are l = 15 and w = 5
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