Liang Xiao possesses Lagerstroemia indica.

According to the meaning of the question, let the width of the path be xm:

( 16-2x)( 12-2x)= 1？ 2? × 16× 12,

Solve this equation: x 1=2, x2 = 12.

However, ∴x=2.= 12 does not meet the meaning of the question and should be omitted. ∴ x = 2.

∴ Liang Xiao's scheme does not meet the requirements, and the width of the road is 2m.

(2) For the figure on the left, take the midpoint of the upper side as the vertex of the triangle, and the two long endpoints of the lower side as the other two vertices of the triangle, and the area of the triangle is equal to half the area of the rectangle;

There are two paths on the right, horizontal and vertical, each with the same width. When the width of the path is 4 meters, the remaining area except the path is half of the distance area.