Final Answer:
The length of side BD in quadrilateral ABCD is C) 6.5 cm.
Step-by-step explanation:
In quadrilateral ABCD, we can use the triangle inequality theorem to determine the possible range of lengths for side BD.
According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider triangle ABC with sides AB, BC, and AC.
Applying the triangle inequality, we find that (AB + BC > AC), which translates to (5 + 4 > 5.5). This condition is satisfied.
Now, let's consider triangle ACD with sides AC, CD, and DA. Applying the triangle inequality, we find that (AC + CD > DA), which translates to (5.5 + 3.5 > 2.5).
This condition is also satisfied.
Therefore, both conditions are met, indicating that side BD can connect points B and D to form a valid quadrilateral.
The length of side BD is the difference between the sum of the lengths of sides AB and CD and the length of side AC: ( (AB + CD) - AC = (5 + 3.5) - 5.5 = 6.5 \) cm.
In summary, the correct answer is C) 6.5 cm.