1969 Canadian MO Problems/Problem 3
Problem
Let be the length of the hypotenuse of a right triangle whose two other sides have lengths and . Prove that . When does the equality hold?
Solution
By the Pythagorean Theorem and the trivial inequality, .
Thus Since are all positive, taking a square root preserves the inequality and we have our result.
For equality to hold we must have . In this case, we have an isosceles right triangle, and equality certainly holds for all such triangles.
1969 Canadian MO (Problems) | ||
Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • | Followed by Problem 4 |