Answer:
(A) 5.5 units
Explanation:
Given: Diameter AC intersects chord BD at point E such that AE = 2.5 units and DE = 3.4 units. Point O is the center of the circle, and the radius of the circle is 5 units. we have to find the approximate length of BE.
Now, CE=CO+OE=5+(OA-AE)=5+2.5=7.5 units.
Now, by Intersecting Chord Theorem which states that when two chords intersect each other inside a circle then the products of their segments are equal.
Thus,

Substituting the given values, we get



≈

therefore, the measure of DE is 5.5 units.
Hence, option A is correct.