Triangle?
Geometry
Level
3
Find the area of a right triangle whose hypotenuse length is 10 and whose altitude to the hypotenuse is 6.
30
Other
45
Triangle doesn't exist
60
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1 solution
Any right triangle has its hypotenuse as the diameter of its circumcircle. This circle will have radius 5 (half the diameter). Consequently the maximum altitude of the vertex opposite to the diameter is 5, hence the suggested triangle is nonexistent.