What is the area of the triangle?

In summary, the conversation discusses a geometry problem involving finding the area of a triangle with given median lengths. The solution involves using the barycenter and symmetric point of the triangle, and ultimately the area is found to be 8.
  • #1
Hessam
36
0
First of all note this is NOT HOMEWORK

This is an interesting geometry problem my old statistics and discrete math teacher gave to me, i solved it, however i just wanted to give it out... very tough problem (at least for me, probably easy for most poeple here)

You have a triangle... the lengths of the three medians are
Ma = 3
Mb = 4
Mc = 5

so what is the area of the triangle?

good luck
 
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  • #2
Hi!

I'm not a native english speaking person so I don't get the "median" part. Do you mean length of the sides?
 
  • #3
No, he means the lengths of the medians which are the lines that pass from one corner to the mid point of the opposite sides. It isn't a particularly difficult question if you know how to describe the areas of triangles in terms of sides (at least on first inspection it seems there is an obvious argument to try).
 
  • #4
Hessam said:
...so what is the area of the triangle?

Let G be the barycenter of ABC, and let P be its symmetric point with respect to middle point of BC.

Then, the triangle BGP is formed by 2/3 of the medians (and it is rectangle).

So, BGParea = (2/3)^2 * (3*4)/2 = 8/3 .

But BGP is 1/3 of ABC.

So, ABCarea is 8.
 
Last edited:

What is an interesting geometry problem?

An interesting geometry problem is a mathematical puzzle or challenge that involves the use of geometric concepts and principles. These problems often require critical thinking and problem-solving skills to solve.

What makes a geometry problem interesting?

A geometry problem can be considered interesting if it is challenging, involves creative thinking, has multiple possible solutions, or has real-world applications.

What are some examples of interesting geometry problems?

Some examples of interesting geometry problems include the Seven Bridges of Königsberg problem, the Monty Hall problem, and the Apollonian gasket problem. There are also many interesting geometry puzzles and brain teasers that can be found online or in puzzle books.

How can I solve an interesting geometry problem?

To solve an interesting geometry problem, it is important to understand the given information and apply geometric principles and formulas. Sometimes, it may be helpful to draw a diagram or use visual aids to better understand the problem. Additionally, thinking outside the box and trying different approaches can lead to a solution.

Why are geometry problems important?

Geometry problems are important because they help develop critical thinking and problem-solving skills. They also provide a practical application of geometric principles and can improve spatial reasoning and visualization abilities. Furthermore, solving interesting geometry problems can be a fun and challenging way to exercise the brain.

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