Geometry · Pythagorean theorem · Altitudes · Foot of an altitude · Consecutive integers · Difference of squares
The lengths of the sides of a triangle are three consecutive natural numbers, each greater than \(3\). The altitude drawn to the middle side splits that side into two segments. Prove that the lengths of these two segments differ by \(4\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Regional Competition (Okruzno takmicenje) 1996, high school grade I, problem 2. The 1996 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS). Source