请解答---Question Number: 4 Question Stem: 如图, 在矩形 ABCD 中, M 为 BC 边上一点, 连接 AM, 过点 D 作 DE ⊥ AM 于 E, 若 DE = DC = √5, AE = 2EM, 则 CM 的长为 ( ) Translation of Question Stem: As shown in the figure, in rectangle ABCD, M is a point on side BC. Connect AM. Draw DE perpendicular to AM from point D, intersecting AM at E. If DE = DC = √5 and AE = 2EM, then the length of CM is ( ). Given Information: 1. ABCD is a rectangle. 2. M is a point on side BC. 3. DE ⊥ AM at E. 4. DE = DC = √5. 5. AE = 2EM. Quantity to Find: The length of CM. Options: A. √5 / 2 B. 3 / 2 C. 1 D. 2 Chart/Diagram Description: - Type: Geometric figure (Rectangle and related line segments). - Main Elements: - Rectangle ABCD with vertices labeled A, B, C, D in counterclockwise order. - Point M is located on the side BC, between B and C. - Line segment AM connects vertex A to point M. - Line segment DE is drawn from vertex D to a point E on AM. - There is a right angle symbol at point E, indicating that DE is perpendicular to AM. - All vertices A, B, C, D and points E, M are labeled. - Lines: Straight lines form the sides of the rectangle (AB, BC, CD, DA) and the segments AM and DE. DE is perpendicular to AM. - Shapes: A rectangle ABCD. Triangles are formed, such as △ABM, △ADM, △CDM, △ADE, △DEM. A right angle is marked at E (∠DEA = 90°).