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

• October 23rd 2012, 05:27 PM
Cacia
Please, could someone help me with this Optimization problem?
What is the largest possible area for a triangle whose hypotenuse is 5cm. long?
• October 23rd 2012, 05:36 PM
Prove It
Re: Please, could someone help me with this Optimization problem?
Quote:

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.