Question

gerry wants to construct a triangle with segments that are 4, 6, and 11 inches long. which is true about gerrys plan?
gerry can construct one unique triangle with these side lengths.
gerry can construct exactly two triangles with these side lengths.
gerry can construct more than one triangle with these side lengths.
gerry cannot construct a triangle with these side lengths.

Explanation:

Step1: Apply triangle inequality theorem

For three side lengths \(a\), \(b\), and \(c\) to form a triangle, \(a + b>c\), \(a + c>b\), and \(b + c>a\) must all hold. Let \(a = 4\), \(b = 6\), \(c = 11\).
Check \(a + b>c\): \(4+6 = 10\), and \(10<11\).

Answer:

Gerry cannot construct a triangle with these side lengths.