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Thread: Please, could someone help me with this Optimization problem?

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    Please, could someone help me with this Optimization problem?

    What is the largest possible area for a triangle whose hypotenuse is 5cm. long?
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    Re: Please, could someone help me with this Optimization problem?

    Quote Originally Posted by Cacia View Post
    What is the largest possible area for a triangle whose hypotenuse is 5cm. long?
    Since it has a hypotenuse, we'll assume that it's right-angled. Call the base of the triangle \displaystyle \begin{align*} x \end{align*}, then the height must be \displaystyle \begin{align*} \sqrt{25 - x^2} \end{align*} by Pythagoras.

    So the area is \displaystyle \begin{align*} \frac{1}{2} x\,\sqrt{25 - x^2} \end{align*}. Differentiate this, set the derivative equal to 0, solve for x, then evaluate the area at this value of x.
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