In the analysis of this problem, the number of AB and BC line segments on both sides of the rectangle is first determined, and then the number of AB and BC line segments is multiplied to obtain the total number of rectangles.
But the number of squares is counted in the whole calculation process, if the AB length is 1, BC can not take 1, AB length is 2, BC can not take 2, AB length is 3, BC can not take 3, AB length is 4, BC can not take 4, in the calculated total need to remove the number of graphics with equal length and width, the answer to this question contains the number of squares.
Therefore, when solving this problem, you can use the enumeration tree to find the number according to the 5 possibilities of AB.
When AB is 5, AD takes a value of 1.2.3.4, AB has one line segment, AD has 10 line segments,
When AB is 4, AD takes a value of 1.2.3, AB has two types of segments, AD has 9 types of segments, and the total number has 18,
When AB is 3, AD takes a value of 1.2.4, AB has 3 types of line segments, AD has 8 kinds of line segments, and the total number has 24 kinds.
When AB is 2, AD takes a value of 1.3.4, AB has 4 types of segments, AD has 7 types of segments, and the total number has 28,
When AB is 1, AD takes a value of 2.3.4, AB has 5 types of segments, AD has 6 types of segments, and the total number has 30.
In total, 110 kinds of rectangles can be derived.
You can also use the total number of graphs to subtract the number of squares, the total number is 15× 10 = 150, and the number of squares is 40, so that the answer is 110.
What do you think of this?
