如图所示，在矩形ABCD中，AB=5，BC=4，E,F分别是AD,BC的中点，点P,Q在EF上，且满足PQ=2，则四边形APQB周长的最小值为---**1. Textual Information:** * **Question Stem:** 2. 如图所示，在矩形ABCD中，AB=5，BC=4，E,F分别是AD,BC的中点，点P,Q在EF上，且满足PQ=2，则四边形APQB周长的最小值为___. * **English Translation of Question Stem:** 2. As shown in the figure, in rectangle ABCD, AB=5 and BC=4. E and F are the midpoints of AD and BC respectively. Points P and Q are on EF, and PQ=2. What is the minimum perimeter of quadrilateral APQB? * **Mathematical Information/Constants:** * AB = 5 * BC = 4 * E is the midpoint of AD. * F is the midpoint of BC. * P and Q are points on line segment EF. * PQ = 2 * The quadrilateral is APQB. **2. Chart/Diagram Description:** * **Type:** Geometric figure (a rectangle with internal line segments and points). * **Main Elements:** * **Shapes:** A rectangle labeled ABCD. * **Points:** * A, B, C, D are the vertices of the rectangle. A is at the bottom-left, B at the bottom-right, C at the top-right, and D at the top-left. * E is a point on the side AD. * F is a point on the side BC. * P and Q are points on the line segment EF, with P shown to the left of Q. * **Lines/Segments:** * The four sides of the rectangle: AB, BC, CD, DA. * A horizontal line segment EF, connecting point E on AD to point F on BC. * Segments AP, PQ, QB, and BA form the quadrilateral APQB. * An additional line segment DP is drawn, connecting D to P. * **Labels and Annotations:** * The length of side AB is labeled "5" below the segment AB. * The length of side BC is labeled "4" next to the segment BC. * The length of segment CF is labeled "2" next to it. * The length of segment BF is labeled "2" next to it. * The length of segment PQ is labeled "2" above the segment PQ. * **Relative Position and Direction:** * E and F are midpoints: E divides AD into two segments of length 2 (AE=ED=2), and F divides BC into two segments of length 2 (BF=FC=2). This is consistent with BC=4. * EF is parallel to AB and CD. * Points P and Q are located on the segment EF.