Here is a geometry puzzle to everyone.How can you cut a rectangular sheet which has a rectangular hole in it, into 2 parts of equal area?I need a general solution for this. The rectangular hole in the rectangular sheet can be oriented(or turned) in any direction (for ex. in the shape of a rhombus) and can lie anywhere in the rectangle( like in the center, at the ends, or corners..).In any case, how should be the cutting line so that it cuts the rectangular sheet with rectangular hole into 2 parts of equal area.This was my interview question in a company, and I was not able to answer it.But latter I found the answer.
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“ Inverse Or Reverse”
Please let me say what their difference is.
Both of them have “verse”, but their difference is between “re” and “in”!
Thanks Dear Ensie, your explanation was so useful.
If we want consider your sentences (… We draw another hole or point in an “upside down” position of that.) we must focus on adjective’s explanation of each one. And according to what you wrote I think both of them can be true.
You guys are really great. I'm glad that I found you guys.
Thanks for the co-operation and the time you spent on this puzzle. And the above discussion is really helpful. Thanks a lot, friends.
Ans: Any line that passes through the center of a rectangular sheet divides the sheet into two equal parts. So the resultant number of ways is infinite.
Similarly, Any line which passes through the centers of the outer rectangle and the inner rectangle(hole) cuts the whole sheet into two equal parts.The resultant parts will be symmetrical also.
that's it. I Broke the ice.
And I did not answer this puzzle in my interview, but I got the job.Lucky ha!!.
Thanks a lot my dear friends.
That’s very kind of you Naresh.
So, according to your answer we must consider a point in the center of the main rectangle and the other point in the center of that hole, then draw a line which passes through these points and continue it to cut the sides of the main rectangle. Do I understand it correct?
I’m so glad that you could get the job finally. I think that your manager must be so nice. Because S/he found out you would find the true answer after some time.
Thanks Naresh. I think that I understand the question well, now.
I have an idea about it.
We can follow these stages:
1- Count the area of the main rectangular.
2-Count the area of that hole.
3-Subtract those areas from each other.
4-Divide that got number into 2 equal areas.
5-Then we try to draw a line according to it.
For example think that the length of the main rectangular is 7 and its width is 3 and also the length of the hole is 3 and its width is 1. According to that way, we will have these stages:
1-The area of the main rectangular: 7*3=21
2-The area of the hole is: 3*1=3
3-Subtracting: 21-3=18
4-Dividing: 18/2=9
5-Now we can make a triangle that its height is 3 and its norm ( I mean the other side that we need for counting its area) is 6.
Yes Ensie! Yo are right!
And also If we have the hole like a rectangular, according to your saying we must put those points in the center of them. In this way we can have 2 equal part exactly.
Good Dear!
Replies
Please let me say what their difference is.
Both of them have “verse”, but their difference is between “re” and “in”!
Thanks Dear Ensie, your explanation was so useful.
If we want consider your sentences (… We draw another hole or point in an “upside down” position of that.) we must focus on adjective’s explanation of each one. And according to what you wrote I think both of them can be true.
You guys are really great. I'm glad that I found you guys.
Thanks for the co-operation and the time you spent on this puzzle. And the above discussion is really helpful. Thanks a lot, friends.
Ans: Any line that passes through the center of a rectangular sheet divides the sheet into two equal parts. So the resultant number of ways is infinite.
Similarly, Any line which passes through the centers of the outer rectangle and the inner rectangle(hole) cuts the whole sheet into two equal parts.The resultant parts will be symmetrical also.
that's it. I Broke the ice.
And I did not answer this puzzle in my interview, but I got the job.Lucky ha!!.
Thanks a lot my dear friends.
So, according to your answer we must consider a point in the center of the main rectangle and the other point in the center of that hole, then draw a line which passes through these points and continue it to cut the sides of the main rectangle. Do I understand it correct?
I’m so glad that you could get the job finally. I think that your manager must be so nice. Because S/he found out you would find the true answer after some time.
Thank you
Your answer is always right in my idea.
I have an idea about it.
We can follow these stages:
1- Count the area of the main rectangular.
2-Count the area of that hole.
3-Subtract those areas from each other.
4-Divide that got number into 2 equal areas.
5-Then we try to draw a line according to it.
For example think that the length of the main rectangular is 7 and its width is 3 and also the length of the hole is 3 and its width is 1. According to that way, we will have these stages:
1-The area of the main rectangular: 7*3=21
2-The area of the hole is: 3*1=3
3-Subtracting: 21-3=18
4-Dividing: 18/2=9
5-Now we can make a triangle that its height is 3 and its norm ( I mean the other side that we need for counting its area) is 6.
And also If we have the hole like a rectangular, according to your saying we must put those points in the center of them. In this way we can have 2 equal part exactly.
Good Dear!
But I'm not able to understand the last point.
So you are going to draw a triangle whose height is 3, but what is the base length??
Area of triangle = 1/2 * base * height.
Where should the triangle be located. Is it in the center, corners?where exactly?
And how do u know where to locate the triangle in any case?
Anyways Sahar, only one straight line is enough to cut the rectangle into 2 equal parts.
But how should it pass..?
Thanks for trying..good friend.
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