Final answer:
The length of the median |EF| of the isosceles trapezoid ABCD is determined to be 14cm after calculating the average of the two base lengths and solving for x.
Step-by-step explanation:
To find the length of the median |EF| of the isosceles trapezoid ABCD, we need to understand that the median of a trapezoid is parallel to the bases and its length is the average of the lengths of the two bases. The median |EF|, therefore, is given by:
(|AB| + |DC|) / 2
We are given |AB| = 2x + 1cm and |DC| = 3x + 2cm. So:
(2x + 1 + 3x + 2) / 2
This simplifies to:
(5x + 3) / 2
Since we know |EF| = 2x + 4cm, we can set up the equation:
(5x + 3) / 2 = 2x + 4
Solving for x gives:
5x + 3 = 4x + 8
x = 5
Substituting x back into the expression for |EF|:
|EF| = 2(5) + 4 = 14cm
Therefore, the correct answer for the length of median |EF| is 14cm, which corresponds to option B.