Question

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

Explanation:

Step1: Recall Triangle Inequality

The triangle inequality theorem states that for three side lengths \(a\), \(b\), \(c\) (where \(c\) is the longest side), the sum of the two shorter sides must be greater than the longest side: \(a + b>c\).

Step2: Identify Sides

Given sides: \(40\) cm, \(60\) cm, \(100\) cm. The longest side \(c = 100\) cm, and the two shorter sides \(a = 40\) cm, \(b = 60\) cm.

Step3: Apply Inequality

Calculate \(a + b\): \(40+60 = 100\) cm. The triangle inequality requires \(a + b>c\), but here \(40 + 60=100\), which does not satisfy \(a + b>c\) (it's equal, not greater). So, no triangle can be formed.

Answer:

no triangle