Question

How do you find the area of the largest isosceles triangle having a perimeter of 18 meters?

Answer 1

Use Lagrange multiplier
[https://en.wikipedia.org/wiki/Lagrange_multiplier]

Explanation:

Using the wikipwdia notation:
f(x,y)-function that you want to maximize (area of the triangle)
g(x,y)- function that is your "bond" (perimeter) written in equation form g(x,y)=0
`L(x,y, lambda) =f(x,y)-lambda*g(x,y)`
Maximaze `L(x,y,lambda)`:

1. `(partial L)/(partial x)=0`
2. `(partial L)/(partial y)=0`
3. `(partial L)/(partial lambda)=0`

express `x, y or lambda` end put it in the 3. equation