Assumptions, Assumptions
Geometry
Level
2
A right triangle has two sides of length 3 and 4.
How many possible values are there for the length of the hypotenuse?
None
Only one
At least three
Exactly two
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1 solution
Relevant wiki: Pythagorean Theorem
There are two possibilities: a 3 − 4 − 5 triangle and a 7 − 3 − 4 triangle. Thus, the number of ways is 2 .
Note: we can't have more because the only other possibility is that 3 is the hypotenuse, however, that would mean that 4 is a side length, which violates the Pythagorean Theorem.