Question

which best describes the triangle or triangles, if any, that can be formed with sides measuring 60 centimeters, 100 centimeters, and 40 centimeters? infinitely many similar scalene triangles. one unique scalene triangle no triangle two unique scalene triangles

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let \(a = 40\), \(b = 60\), and \(c = 100\).

Step2: Check the inequalities

Check \(a + b>c\), \(a + c>b\), and \(b + c>a\). Calculate \(a + b=40 + 60=100\), and \(c = 100\). Since \(a + b = c\) (i.e., \(40+60 = 100\)), the triangle - inequality theorem is violated.

Answer:

no triangle