Question

How many triangles can be constructed with sides measuring 5 m, 16 m, and 5 m?

Responses

none
none

more than one
more than one

one

Answer 1

To determine how many triangles can be constructed with sides measuring 5 m, 16 m, and 5 m, we can apply the Triangle Inequality Theorem. According to this theorem, for three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's denote the sides as \( a = 5 \, m \), \( b = 5 \, m \), and \( c = 16 \, m \).

Now we check the inequalities:

1. \( a + b > c \):
\[
5 + 5 > 16 \rightarrow 10 > 16 \quad \text{(false)}
\]

2. \( a + c > b \):
\[
5 + 16 > 5 \rightarrow 21 > 5 \quad \text{(true)}
\]

3. \( b + c > a \):
\[
5 + 16 > 5 \rightarrow 21 > 5 \quad \text{(true)}
\]

Since the first inequality fails, the sides 5 m, 16 m, and 5 m cannot form a triangle.

Thus, the correct response is **none**.