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:
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\( a + b > c \): \[ 5 + 5 > 16 \rightarrow 10 > 16 \quad \text{(false)} \]
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\( a + c > b \): \[ 5 + 16 > 5 \rightarrow 21 > 5 \quad \text{(true)} \]
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\( b + c > a \): \[ 5 + 16 > 5 \rightarrow 21 > 5 \quad \text{(true)} \]
Since the first inequality fails, the sides 5 m, 16 m, and 5 m cannot form a triangle.
Thus, the correct response is none.