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Optimal Triangles

What is the largest possible area that can be found in a triangle with perimeter 12? We will call this shape an optimal triangle for this exploration.

What are some properties of the optimal triangles? What is another name for this triangle?

Try this exploration again, but try a different perimeter. Is the optimal triangle the same or different? Do you think the results of the exploration will be the same, regardless of the perimeter used? Explain why or why not.

 Related External Resources

Heron's Area of a Triangle
This site will take you through some historical explorations, some interactive activities, and some intriguing connections in mathematics.

Geoboards in the Classroom
This unit deals with the side lengths and area of two-dimensional geometric figures using the geoboard as a pedagogical device.

Minimum Perimeter of an Inscribed Triangle
Given a circle of unit radius, what's the perimeter of the smallest triangle whose vertices are on the circle and which contains the center of the circle?

How Many Triangles Have Sides Whose Lengths Total 15?
How many triangles can one construct with integral sides adding up to 15?

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