Optimization of a fence around a triangular pen

[ucfkid1090]

Homework Statement

A farmer wishes to enclose a pen in the shape of a right triangle with 100 ft of fencing. Set up the equation to find the maximum and minimum dimensions but do not solve the problem.

Homework Equations

I know the area for a triangle is simply A=1/2B*H and that the constraint is B+H+C=100 but I don't know how to solve the equation with 4 unknowns. This is a sample test problem but on the test we may also be required to solve it so if someone could help me set it up and solve it I would appreciate it. Thanks

 

[Eynstone]

There are just two variables involved as C^2=B^2 + H^2.

 

[ucfkid1090]

ok so then if my substitution is correct I should get a formula of (b+h)+sqrt(b^2+h^2)=100