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Math Help - Calculus Optimizing Problem--Held Needed

  1. #1
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    Calculus Optimizing Problem--Held Needed

    Hi, I need some help on how to do the following question.

    Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12 cm. The two sides of the rectangle lie along the legs

    Final Answer: 15cm squared
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  2. #2
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    Use similar triangles.

    A=xy

    But by similar triangles, x/5=(12-y)/12

    So, y=12-(12x/5)

    A=x(12-(12x/5))

    dA/dx=12-(24x/5)

    12-(24x/5)=0

    x=5/2 and y=6

    A=xy=(5/2)(6)=15
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