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Four horizontal lines and four vertical lines are drawn in a plane. In how many ways can four lines be chosen such that a rectangular region

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Four horizontal lines and four vertical lines are drawn in a plane. In how many ways can four lines be chosen such that a rectangular region is enclosed?

Apr 2, 2015

#1
+5

Four vertical lines and four horizontal lines enclose a 3 x 3 rectangle. How many separate rectangles of all sizes are there?

Individually, there will be

9 1 x 1 rectangles (1 space down and 1 space across)

6 1 x 2 rectangles (1 space down and 2 spaces across)

6 2 x 1 rectangles

3 1 x 3 rectangles

3 3 x 1 rectangles

4 2 x 2 rectangles.

2 2 x 3 rectangles

2 3 x 2 rectangles

1 3 x 3 rectangles

Total:  36 rectangles.

Apr 2, 2015

#1
+5

Four vertical lines and four horizontal lines enclose a 3 x 3 rectangle. How many separate rectangles of all sizes are there?

Individually, there will be

9 1 x 1 rectangles (1 space down and 1 space across)

6 1 x 2 rectangles (1 space down and 2 spaces across)

6 2 x 1 rectangles

3 1 x 3 rectangles

3 3 x 1 rectangles

4 2 x 2 rectangles.

2 2 x 3 rectangles

2 3 x 2 rectangles

1 3 x 3 rectangles

Total:  36 rectangles.

geno3141 Apr 2, 2015