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Math Help - quadratic algebra

  1. #1
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    quadratic algebra

    a farmer has 60m of fencing with which to construct three sides of a rectangular yard connected to an existing fence.
    a. if the width of the paddock is x m and teh area inside the yard, A m^2, write down teh rule connecting A and x
    b. determine teh maximum area that can be formed for the yard.

    ( the side of existing fence is a length)

    please help me i have an exam tomorrow on this!!!
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  2. #2
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    Quote Originally Posted by summna09 View Post
    a farmer has 60m of fencing with which to construct three sides of a rectangular yard connected to an existing fence.
    a. if the width of the paddock is x m and teh area inside the yard, A m^2, write down teh rule connecting A and x
    b. determine teh maximum area that can be formed for the yard.

    ( the side of existing fence is a length)

    please help me i have an exam tomorrow on this!!!
    Hello,

    a) first make a sketch of the situation.

    Since the length of the fence is 60 m the length of the rectangle is:

    l = 60 -2x

    You are supposed to know that the area of a rectangle can be calculated by

    A= l \cdot w~\implies~A(x)=(60-2x) \cdot x

    b) A(x) = -2x^2 + 60x . A is a quadratic function pointing down, that means the maximum value is at it's vertex:
    In general the x-value is calculated by: x_V=-\frac{b}{2a} With your problem:
    x_V = -\frac{60}{2 \cdot (-2)} = 15

    Thus the rectangle has the dimension: l = 30\ m\ \text{and } w = 15\ m
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