Question

Determine if the given information will form a unique triangle, many different triangles, or no triangles. The problem: 4 in, 5 in, and 2 in.

a) Unique triangle

b) Many different triangles

c) No triangle

d) Insufficient information

Answer 1

The given information forms a unique triangle.

Step-by-step explanation:

In order for the given information to form a triangle, it must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, the given lengths are 4 in, 5 in, and 2 in.

Let's check if the triangle inequality theorem is satisfied:

4 + 5 > 2

5 + 2 > 4

2 + 4 > 5

Since all three inequalities are satisfied, the given information forms a unique triangle.