Question

using the triangle inequality theorem, can a triangle be formed with side lengths of 2 cm, 2 cm, and 5 cm?
a. depends on the angle between them
b. yes
c. only if its a right triangle
d. no

Explanation:

Step1: Recall Triangle Inequality Theorem

For three side lengths \(a\), \(b\), \(c\) of a triangle, the following must hold: \(a + b>c\), \(a + c>b\), and \(b + c>a\)
Let \(a = 2\), \(b = 2\), \(c = 5\)

Step2: Check \(a + b>c\)

\(2+2 = 4\)
Since \(4<5\) (i.e., \(a + b = 4\) and \(c = 5\)), the Triangle Inequality Theorem is violated.

Answer:

d. No