3 statements, one false, right triangle (2020 Novosibirsk Oral Geo Oly 8.3)
Source:
May 20, 2021
geometryright triangle
Problem Statement
Maria Ivanovna drew on the blackboard a right triangle with a right angle . Three students looked at her and said:
Yura said: "The hypotenuse of this triangle is cm."
Roma said: "The altitude drawn from the vertex on the side is cm."
Seva said: "The area of the triangle is cm."
Determine which of the students was mistaken if it is known that there is exactly one such person.