2019 · Q77
Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AOnly one
- BOnly two
- COnly three
- DInfinitely many
Explanation
n^2 + (n+1)^2 = (n+2)^2 gives n^2 − 2n − 3 = 0, i.e. (n−3)(n+1) = 0. The only positive solution is n = 3, giving the single triple (3, 4, 5).