Four lattices are selected from the 5x4 grid borad indicated so they form the corners of a rectangle having sides parallel to edges of the board. How many different rectangles can be formed in this way?
答案:150
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數學問題~~~~
2007-09-18 3:49 am
回答 (1)
2007-09-19 1:30 am
✔ 最佳答案
a) Let us use the (x,y) co-ordinates to name the grid where (0,0) being the bottom left corner of the grid.b) Consider (0,0) being the bottom left corner of a rectangle, 20 rectangles can be formed.
Consider (0,1) being the bottom left corner of a rectangle, 15 rectangles can be formed.
Consider (0,2) being the bottom left corner of a rectangle, 10 rectangles can be formed.
Consider (0,3) being the bottom left corner of a rectangle, 5 rectangles can be formed.
Subtotal1=20+15+10+5.
b) Consider (1,0) being the bottom left corner of a rectangle, 16 rectangles can be formed.
Consider (1,1) being the bottom left corner of a rectangle, 12 rectangles can be formed.
...... Subtotal2=16+12+8+4.
............
c) Following this line of thought, you can get to the answer of 150.
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