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Charlene C.

asked • 04/03/16

A rectangle is divided by m lines parallel to one pair of opposite sides and n lines parallel to the other pair.

 
The question is: A rectangle is divided by m lines parallel to one pair of opposite sides and n lines parallel to the other pair. How many rectangles are there in the figure obtained?
 
So far, I have only got (l/m -1) is the no. of vertical rectangle segments if length of rectangle be l 
and I also got that w/n +1 where this denotes the number of horizontal segments. where w is the width of the rectangle.
I tried to multiply these two together, but I didn't get the correct answer. The correct answer is 
[(m+2)(m+1) (n+1) (n+2)]/4 how? 

1 Expert Answer

By:

Mark M. answered • 04/03/16

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Charlene C.

Thx @Mark M. But where does the divided by 4 in the answer come from?
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04/03/16

Mark M.

Have absolutely no idea.
Let's say there are 2 m lines and 2 n lines. We can see 9 rectangles.
Plugging these values into the "answer:"
(4)(3)(3)(4) / 4
144 / 4
36
There are not 36 rectangles!!!
This is a counterexample to the "answer."
 
 
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04/03/16

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