Question

question 37 of 50
the hypotenuse is always the shortest side of a triangle.
false
true

Explanation:

In a right - triangle, the hypotenuse is the side opposite the right angle. By the Pythagorean theorem, for a right - triangle with legs of length \(a\) and \(b\) and hypotenuse of length \(c\), \(c=\sqrt{a^{2}+b^{2}}\). Since \(a^{2}\) and \(b^{2}\) are positive, \(c\) must be greater than both \(a\) and \(b\). So the hypotenuse is the longest side of a right - triangle, not the shortest. Also, the term "hypotenuse" is only defined for right - triangles. But in general, for any triangle (right - triangle or not, but hypotenuse is specific to right - triangles), the statement that the hypotenuse is always the shortest side is false.

Answer:

A. False