Can a triangle be formed with these length constraints?

[Nipuna Weerasekara]

Homework Statement

There is a triangle with sides $$ 3,3r,3r^2 $$ such that 'r' is a real number strictly greater than the Golden Ratio.
Is this statement true or false...?

Homework Equations

$$Golden \space Ratio = \phi = 1.618... $$

The Attempt at a Solution

Actually I have no clue at all how to approach to this kind of question.

 

[member 587159]

Homework Statement

There is a triangle with sides $$ 3,3r,3r^2 $$ such that 'r' is a real number strictly greater than the Golden Ratio.
Is this statement true or false...?

Homework Equations

$$Golden \space Ratio = \phi = 1.618... $$

The Attempt at a Solution

Actually I have no clue at all how to approach to this kind of question.

When I give you 3 line segments with a random length, can you make a triangle with it?

 

[Nipuna Weerasekara]

When I give you 3 line segments with a random length, can you make a triangle with it?

I guess so

 

[micromass]

Take a paper, try to make a triangle with sides 1cm, 1cm and 10cm. Show us the triangle you found.

 

[Nipuna Weerasekara]

Actually there is a theorem called triangle inequality theorem, which states given ABC triangle, which has a,b,c length sides a+b>c , a+c>b and b+c>a must be true. therefore no need to show it to you that I can't create a triangle out of those sides 1,1 and 10.

 

[Nipuna Weerasekara]

Actually this gives me an idea how to approach the question.
i can try to get a result for r by solving three inequalities
$$3r^2 +3 > 3r$$ $$3r^2+3r>3$$ $$3+3r>3r^2$$

 

[Nipuna Weerasekara]

Eventually one inequality leads that r has a complex variance. (by solving 3r^2 +3 > 3r)

 

[micromass]

Eventually one inequality leads that r has a complex variance. (by solving $$3r^2 +3 > 3r$$)

Is,'t that trvially satisfied?

 

[Nipuna Weerasekara]

Is,'t that trvially satisfied?

I don't get what you say here.

 

[Nipuna Weerasekara]

But in a sense I can say that r is not strictly a real number hence the statement is false... Am I right?

 

[Nipuna Weerasekara]

No I was wrong all along... I solved it. The statement is true. All r is real and greater than Golden Ratio (1.61803)...

 

[fresh_42]

The statement is true. All r is real and greater than Golden Ratio (1.61803)...

So $r=10$ is obviously greater than $\phi$ and you've found a triangle with sides $3, 30$ and $300$?
Which curvature do you assume your geometry has?