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Printjmc
geometry senior
Problem
A triangle can be formed having side lengths and It is impossible, however, to construct a triangle with side lengths and Using the side lengths and how many different triangles with exactly two equal sides can be formed?
Solution
The sum of any two sides of a triangle must be bigger than the third side.
(When two sides are known to be equal, we only need to check if the sum of the two equal sides is longer than the third side, since the sum of one of the equal sides and the third side will always be longer than the other equal side.)
If the equal sides were both equal to the third side must be shorter than The possibility from the list not equal to (since we cannot have three equal sides) is So here there is possibility.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
Thus, in total there are possibilities.
(When two sides are known to be equal, we only need to check if the sum of the two equal sides is longer than the third side, since the sum of one of the equal sides and the third side will always be longer than the other equal side.)
If the equal sides were both equal to the third side must be shorter than The possibility from the list not equal to (since we cannot have three equal sides) is So here there is possibility.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
If the equal sides were both equal to the third side must be shorter than The possibilities from the list not equal to (since we cannot have three equal sides) are and So here there are possibilities.
Thus, in total there are possibilities.
Final answer
14