# Geometric Construction Then Minimize Area

pianocleaner shared this question 2 years ago

Hi,

I'm working on a project and I have to find the minimum area of an equilateral triangle which has one vertex on each of the sides of a 3,4,5 right triangle.

How would I do this with geogebra?

Thanks

1

Triangle équilatéral circonscrit à un triangle 3,4 et 5 ?

1

oder allgemein?

1

moving mm in attached you can see that minimum is when one side of equilateral is over minimum side of 345 triangle

really the problem can be maximum

minimum=12.20652

maximum=,26.43376

Files: foro.ggb
1

Hi,

hmm, I think, that the equilateral triangle should be inside the 3-4-5-triangle ...

Solution with CAS ≈ 1.36

1

a solution by using geometric construction (solution without CAS: 1.36189 )

1

Thanks mire2 could you explain what you are doing? Also how do u use CAS + geometry? is that online CAS or not? cuz when I do online CAS, I cant make segments and stuff

1

Salut,

I hope the attached file explains it better.

Main Idea:

Starting from a point P=(p,0) and finding points with equal distances.

Minimizing this distance

That's it.

Great Job accomplished. 😎