1. ## Please, could someone help me with this Optimization problem?

What is the largest possible area for a triangle whose hypotenuse is 5cm. long?

2. ## Re: Please, could someone help me with this Optimization problem?

Originally Posted by Cacia
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.