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Math Help - Problem solving with Quadratics

  1. #1
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    Exclamation Problem solving with Quadratics

    A triangular paddock has a road AB forming its hypotenuse. AB is 3 km long. The fences AC and CB are at right angles. If BC is 400 m longer than AC, find the area of the paddock in hectares.
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  2. #2
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    Quote Originally Posted by Tessarina View Post
    A triangular paddock has a road AB forming its hypotenuse. AB is 3 km long. The fences AC and CB are at right angles. If BC is 400 m longer than AC, find the area of the paddock in hectares.
    By Pythagoras:

    AC^2 + CB^2 = AB^2

    but we know that BC = AC + 0.4 (if it is measured in kilometres).


    So AC^2 + (AC + 0.4)^2 = 3^2

    AC^2 + AC^2 + 0.8AC + 0.16 = 9

    2AC^2 + 0.8AC - 9.84 = 0

    AC^2 + 0.4AC - 4.92 = 0.

    Now you can use the Quadratic Formula to find AC.


    Once you have AC, you will have the base and the height of the triangle, so you will be able to find its area.
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    Why was this particular question moved from "Algebra and Prealgebra" while the other questions about quadratic equations were left?
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