http://jwilson.coe.uga.edu/EMAT6680Fa11/Antillanca/EMAT6680.gif


Rayen Antillanca. Assignment 6


 

Construct the triangle with minimum perimeter inscribed in a given triangle.

The inscribed triangle with minimum perimeter is constructed with the heights of the original triangle.

 

 

Let ABC be any triangle

http://jwilson.coe.uga.edu/EMAT6680Fa11/Antillanca/Assignment6/t1.gif

First step construct the heights

 

http://jwilson.coe.uga.edu/EMAT6680Fa11/Antillanca/Assignment6/t2.gif

 

Second step, construct a new triangle joining the three bases of the heights

http://jwilson.coe.uga.edu/EMAT6680Fa11/Antillanca/Assignment6/t3.gif

Therefore, triangle DEF is the triangle with minimum perimeter

 

To prove that this triangle is the minimum perimeter you can draw another triangle and compare these perimeters. The next GSP file shows this.

 

 

Note: All figures on this web page were made with The Geometerís Sketchpad

 

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