Saturday, April 23, 2011
Sunday, November 28, 2010
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
In the figure, the following inequalities hold.
a + b > c
a + c > b
b + c > a
Example:
Check whether it is possible to have a triangle with the given side lengths.
7, 9, 13
Add any two sides and see if it is greater than the other side.
The sum of 7 and 9 is 16 and 16 is greater than 13.
The sum of 9 and 13 is 21 and 21 is greater than 7.
The sum of 7 and 13 is 20 and 20 is greater than 9.
This set of side lengths not satisfies Triangle Inequality Theorem.
These lengths do form a triangle.
Example:
Check whether the given side lengths form a triangle.
4, 8, 15
Check whether the sides satisfy the Triangle Inequality Theorem.
Add any two sides and see if it is greater than the other side.
The sum of 4 and 8 is 12 and 12 is less than 15.
This set of side lengths does not satisfy Triangle Inequality Theorem.
These lengths do not form a triangle.
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
In the figure, the following inequalities hold.
a + b > c
a + c > b
b + c > a
Example:
Check whether it is possible to have a triangle with the given side lengths.
7, 9, 13
Add any two sides and see if it is greater than the other side.
The sum of 7 and 9 is 16 and 16 is greater than 13.
The sum of 9 and 13 is 21 and 21 is greater than 7.
The sum of 7 and 13 is 20 and 20 is greater than 9.
This set of side lengths not satisfies Triangle Inequality Theorem.
These lengths do form a triangle.
Example:
Check whether the given side lengths form a triangle.
4, 8, 15
Check whether the sides satisfy the Triangle Inequality Theorem.
Add any two sides and see if it is greater than the other side.
The sum of 4 and 8 is 12 and 12 is less than 15.
This set of side lengths does not satisfy Triangle Inequality Theorem.
These lengths do not form a triangle.
Saturday, November 27, 2010
Subscribe to:
Posts (Atom)
