Question

given that de is the length of the mid - segment. what is the length of bc? a 12 b 16 c 24 d 32

Explanation:

Step1: Recall the mid - segment theorem

The mid - segment theorem states that the length of the mid - segment of a triangle (a segment connecting the midpoints of two sides of a triangle) is half the length of the third side. In triangle \(ABC\), \(DE\) is the mid - segment. Let \(DE = 8\).

Step2: Apply the mid - segment formula

According to the formula \(DE=\frac{1}{2}BC\). We can solve for \(BC\) by multiplying both sides of the equation by \(2\). So \(BC = 2\times DE\).
Substitute \(DE = 8\) into the formula: \(BC=2\times8\).

Answer:

\(16\) (Option B)