Optimization of a fence around a triangular pen

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A farmer aims to enclose a right triangular pen using 100 ft of fencing. The area of the triangle is given by A = 1/2 * B * H, with the constraint B + H + C = 100, where C is the hypotenuse. The discussion highlights the challenge of solving the equation with four unknowns. A key insight is that there are only two variables, as C can be expressed using the Pythagorean theorem: C^2 = B^2 + H^2. The proposed substitution leads to the equation (B + H) + sqrt(B^2 + H^2) = 100.
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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
 
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There are just two variables involved as C^2=B^2 + H^2.
 
ok so then if my substitution is correct I should get a formula of (b+h)+sqrt(b^2+h^2)=100
 

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