Browse · MATH
Printjmc
geometry senior
Problem
Dakota randomly selected three different integers through What is the probability that the three numbers selected could be the sides of a triangle? Express your answer as a common fraction.
Solution
There are possible sets of three different integers. We need to figure out how many of these could be the sides of a triangle.
Clearly, none of the sides can be since that would violate the Triangle Inequality. As for the rest, it is quite a simple matter to just list them all in an organized fashion: Therefore, there are possible sets of numbers that could be sides of a triangle, out of possible sets, so our answer is
Clearly, none of the sides can be since that would violate the Triangle Inequality. As for the rest, it is quite a simple matter to just list them all in an organized fashion: Therefore, there are possible sets of numbers that could be sides of a triangle, out of possible sets, so our answer is
Final answer
\frac{7}{20}