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-   -   A triangle has a base 12 feet long and an altitude 8 feet high. Find the area of the (https://www.askmehelpdesk.com/showthread.php?t=595854)

  • Sep 5, 2011, 05:15 AM
    jao10
    A triangle has a base 12 feet long and an altitude 8 feet high. Find the area of the
    A triangle has a base 12 feet long and an altitude 8 feet high. Find the area of the largest rectangle that can be inscribed in the triangle so that the base of the rectangle falls on the base of the triangle.
  • Sep 5, 2011, 08:59 AM
    Unknown008
    Make a sketch, that always helps.

    Let the length of half the base of the rectangle be x and the height of the rectangle be y.

    Let the vertices of the triangle be A, B and C; A and B being at the base. Let the vertices of the rectangle be P, Q, R and S, P and Q being at the base. And then, let X be the midpoint of AB.

    From the information given and your sketch, you should see that:







    The area of the rectangle is given by:



    The optimum of A is obtained when the derivative of A is equal to 0.

    Taking the two equations, we first get A in terms of y only:



    Now, find the derivative of A, set that to 0 and solve for x, the length which is half the base of the rectangle. Then you can find the area of the rectangle.

    Can you post what you get? :)

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