如图,用三种大小不同的5个正方形和1个长方形(阴影部分)拼成长方形ABCD,其中EF = 2,最小的正方形的边长为x.(1)求FG和DG(用含x的代数式表示);(2)用含x的代数式表示长方形ABCD的周长,并求当x = 3时长方形ABCD的周长。---Geometric Figure Description:
Type: Geometric figure / Rectangle dissection.
Main Elements:
* Outer rectangle ABCD with vertices labeled:
* A: Top-left corner.
* B: Bottom-left corner.
* C: Bottom-right corner.
* D: Top-right corner.
* Internal lines divide the rectangle into smaller regions.
* A vertical line segment starts from the top side AD at point H, passes through point F, and continues downwards through point E. The segment appears to extend to the bottom side BC.
* A horizontal line segment starts from the left side AB, passes through point F, and ends at the right side CD at point G.
* Point F is the intersection point of the vertical line segment (through H, F, E) and the horizontal line segment (through F, G).
* Point H is located on the top side AD and on the vertical line segment passing through F and E.
* Point G is located on the right side CD and on the horizontal line segment passing through F.
* Point E is located below point F and on the vertical line segment passing through H and F.
* There is a horizontal line segment passing through point E and ending at point G on the right side CD. This line is below the horizontal line segment FG.
* The region below the horizontal line segment passing through F and G, and to the left of the vertical line segment passing through H, F, and E, is divided into four equal smaller rectangles (visually appearing as squares) placed side-by-side along the bottom edge BC. Three vertical line segments divide this region into the four smaller rectangles.