optimisation using derivatives isoceles triangle..

[Help Meeeeeeeeeeeeeeeeeee]

hey guys, i really need fast help with this question.

A triangular enclosure is to be constructed using 50 metres of fencing (such that the triangular area is isoceles in shape). Find the length of the sides that will maximise the area enclosed and hence find the maximum area.

How do you find the maximum area for this?!?!

(is this in the right place?)

 

[galactus]

Actually, this is more of a calc problem, but you're OK.

The perimeter you are given as P=50.

As the drawing shows, 2x+y=50.

Therefore, y=50-2x. [1]

Set up an eqaution for the area of the triangle.

Can you look at the drawing and see how this was derived using the area of a triangle formula and Pythagoras?.

Our area is:

\(\displaystyle \L\\A=(\frac{y}{2})\sqrt{x^{2}-(\frac{y}{2})^{2}}\)

Sub in [1]:

\(\displaystyle \L\\(\frac{50-2x}{2})\sqrt{x^{2}-(\frac{50-2x}{2})^{2}}\)

=\(\displaystyle \L\\(125-5x)\sqrt{2x-25}\)

Now differentiate, set to 0 and solve for x.

Don't be afraid of the radical It's not that bad. Use the product rule.