Nipuna Weerasekara said: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.
I guess soMath_QED said:When I give you 3 line segments with a random length, can you make a triangle with it?
Is,'t that trvially satisfied?Nipuna Weerasekara said:Eventually one inequality leads that r has a complex variance. (by solving $$3r^2 +3 > 3r$$)
I don't get what you say here.micromass said:Is,'t that trvially satisfied?
So ##r=10## is obviously greater than ##\phi## and you've found a triangle with sides ##3, 30## and ##300##?Nipuna Weerasekara said:The statement is true. All r is real and greater than Golden Ratio (1.61803)...
No, a triangle cannot be formed if all three sides have the same length. This is because in order for a triangle to exist, the sum of any two sides must be greater than the third side. If all three sides have the same length, this condition cannot be met.
Yes, it is possible to form a triangle with only two sides that are equal in length. This type of triangle is called an isosceles triangle. In an isosceles triangle, the two equal sides are opposite of each other and the third side is usually different in length.
The minimum length for the third side to form a triangle is equal to the difference between the sum of the other two sides and the length of the longer side. For example, if the two sides are 3 and 4, the minimum length for the third side would be 4 - (3+4) = 1.
No, a triangle cannot be formed if one side is longer than the sum of the other two sides. This violates the triangle inequality theorem, which states that the sum of any two sides must be greater than the third side for a triangle to exist.
The number of different types of triangles that can be formed with given length constraints depends on the lengths of the sides. If all three sides are different in length, there can be only one type of triangle. If two sides are equal in length, there can be two types of triangles (isosceles and scalene). If all three sides are equal in length, there is only one type of triangle (equilateral).