1969 Canadian MO Problems/Problem 3
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?
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.
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