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The triangle inequality theory means that the two short sides of a triangle has to be greater when added up,than the longer side.

Ex) 2+2=4(for the two smaller sides)

The longer side being 2,so the other two sides are greater.Then can also it be a trinagle.

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What kind of triangle it used to describe for pythagorean inequality theorem?

Obtuse


Given three positive real numbers satisfying the triangle inequalities is it always possible to find a triangle having these as the dimensions?

Sure, that is exactly what the triangle inequality tells us!


What is a statement of the triangle inequality theorem?

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Specifically, if a triangle has sides of lengths (a), (b), and (c), then the following inequalities must hold: (a + b > c), (a + c > b), and (b + c > a). This theorem is fundamental in geometry as it ensures that a valid triangle can be formed with the given side lengths.


The side of a triangle 78cm 20 cm and 22cm find its area?

It is not possible to have a triangle with sides of those lengths. The two shortest sides of a triangle must always add to more than the longest side. This is known as the triangle inequality.


How can we Proof by case to prove triangle inequality?

To prove the triangle inequality using proof by cases, we analyze the possible relationships between the sides of the triangle. For two sides (a) and (b), we consider three cases: when both (a) and (b) are positive, when one is zero, and when one or both are negative. In each case, we show that the sum of the lengths of any two sides is always greater than or equal to the length of the remaining side, thereby satisfying the triangle inequality: (a + b \geq c), (a + c \geq b), and (b + c \geq a). This structured approach confirms the validity of the inequality under all possible scenarios.

Related Questions

What is the triangle inequality?

The triangle inequality theory means that the two short sides of a triangle has to be greater when added up,than the longer side. Ex) 2+2=4(for the two smaller sides) The longer side being 2,so the other two sides are greater.Then can also it be a trinagle.


What does the triangle inequality theorem state?

The triangle inequality theorem states that any side of a triangle is always shorter than the sum of the other two sides.


Can two sides be congruent in the triangle inequality?

no.


What is the statement of the triangle inequality theorem?

jizz in your mouth


How can you use an inequality to describe the dimensions of a figure?

A scalene triangle can be identified by the inequality of the lengths of its sides and size of its angles.


What kind of triangle it used to describe for pythagorean inequality theorem?

Obtuse


What are the basic premises of conflict theory?

Basic premises of conflict theory are "social, political, or material inequality of a social group". So essentially looking at inequality within certain groups.


Given three positive real numbers satisfying the triangle inequalities is it always possible to find a triangle having these as the dimensions?

Sure, that is exactly what the triangle inequality tells us!


Which of the following is the statement of the Triangle Inequality Theorem?

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.


What causes bermudan triangle?

Superstition and conspiracy theory cause the Bermuda Triangle.


What is a statement of the triangle inequality theorem?

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Specifically, if a triangle has sides of lengths (a), (b), and (c), then the following inequalities must hold: (a + b > c), (a + c > b), and (b + c > a). This theorem is fundamental in geometry as it ensures that a valid triangle can be formed with the given side lengths.


The side of a triangle 78cm 20 cm and 22cm find its area?

It is not possible to have a triangle with sides of those lengths. The two shortest sides of a triangle must always add to more than the longest side. This is known as the triangle inequality.