Optimization of a fence around a triangular pen

In summary, the farmer needs to enclose a pen in the shape of a right triangle with 100 ft of fencing. The area of a triangle is A=1/2B*H and the constraint is B+H+C=100. To find the maximum and minimum dimensions, the equation (b+h)+sqrt(b^2+h^2)=100 needs to be solved. However, there are four unknowns in the equation and it may be required to solve it on the test. There are only two variables involved: C^2=B^2 + H^2.
  • #1
ucfkid1090
2
0

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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  • #2
There are just two variables involved as C^2=B^2 + H^2.
 
  • #3
ok so then if my substitution is correct I should get a formula of (b+h)+sqrt(b^2+h^2)=100
 

FAQ: Optimization of a fence around a triangular pen

1. How do you calculate the optimal perimeter for a triangular pen?

The optimal perimeter for a triangular pen can be calculated by using the formula P = a + b + c, where a, b, and c are the lengths of the sides of the triangle. This formula is based on the fact that the perimeter of a triangle is equal to the sum of its three sides.

2. What factors should be considered when optimizing a fence around a triangular pen?

When optimizing a fence around a triangular pen, factors such as the size and shape of the pen, the type and height of the fence, and the materials used should be considered. The purpose of the pen and the animals it will contain should also be taken into account.

3. How can the cost of the fence be minimized while still maintaining its effectiveness?

The cost of the fence can be minimized by carefully selecting the materials and design of the fence. Using more affordable materials and choosing a simple yet effective design can help reduce costs while still maintaining the functionality of the fence.

4. Is there a specific method for determining the optimal placement of the fence around the triangular pen?

There is no specific method for determining the optimal placement of the fence around a triangular pen. However, it is important to ensure that the fence is placed in a way that maximizes the use of the available space and provides adequate protection for the animals inside.

5. How can the stability and durability of the fence be improved?

The stability and durability of the fence can be improved by using sturdy materials, such as metal or high-quality wood, and ensuring that the fence is properly installed and maintained. Adding reinforcements, such as cross-bracing, can also help increase the fence's stability and durability.

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