# Problem on test today

1. Dec 10, 2004

### calvinnn

There was a question on my math test today and i didnt even understand the problem. I want to see if anyone else knows how to do it. So here it goes:
"Use Calculus to prove which vertex angle an isoseles triange the greatest area"

I think your supposed to find a equation for Area and Perimeter. Then take one of the equations and solve for a variable. Plug it into the next equation and then differentiate, like i would do on optimization problems, but i didnt know how to do it with this problem. Below is the figure given.

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2. Dec 10, 2004

### dextercioby

I'm not sure,there might be more to your problem than what i understood:
$$S_{triangle} =\frac{k^{2}\sin\theta}{2}$$,where k and k are the 2 sides of the isosceles triangle assuled constant and the angle $\theta$ is the angle between the 2 congruent segments.
This of S as a function of only one variable,the angle $\theta$ and use the principle of extremum to find the angle for which the area is maximum.Then find that maximum inserting the value for maxmum in the initial function.

As i said,maybe the problem is more complicated,but for now,try to solve it this way.

Daniel.

3. Dec 10, 2004

k thankssss