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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I don’t know its answer really, but if I were you I would use “ inverse” for it.
Let me say that I didn’t know the meaning of “upside down”, but when you used it I searched it in the dictionary and I found out that it’s an adverb and it means: “ With the top part at the bottom”.
For example: when we hang a picture on the wall wrongly so that the top is at the bottom. We will say: " The picture is upside down."
Thanks Naresh.
I said “norm” was 6 cm, but I meant its base. Sorry I didn’t know its name in English before, but I know it now. Thanks for your saying.
Now please pick up a pen and a paper and draw what I will say.
Please draw a rectangular that its length is 7 and its width is 3. Then put a hole in the bottom of its right side, just like one of your pictures. Draw the length of the hole, 3 and its width 1.
Now we want to make a triangular that its area must be 18. So we can suppose 6 for its base and 3 for its height.
Part 6 cm from upper length of the rectangular from its left side.
Now, please draw a straight line from that place to the bottom angle of the left side of the rectangular.
So, we will have a triangular that is 90 degrees in one of its angles.
Its base is on the upper length of the rectangular and its height is on the left width of the rectangular.
And also, the hole won’t be inside our rectangular.
Thanks Naresh.
But in that condition I will try to make a rectangular instead of triangular. That its length will be 3 (It can be on the width of main rectangular) and its breath will be 17/6. Because in that situation we need 8.5 for every part.
7*3=21
2*2=4
21-4=17
17/2=8.5
In fact I will try to make triangular, square or rectangular with one line.
I think it isn’t so important what your answer is ,Dear Ensie. Your trying was admirable in my idea. And of course, your answer means that you at least understand the question!
A picture speaks a thousand words. Both the figures explain about the same puzzle. Don't think they are different puzzles. And yes, we should use only one cutting line. Sorry guys, if you think the explanation is not clear before.However, this is really a good question I came across in one of my interviews. Hope you like it.
I would like to give a hint to this puzzle.
In how many ways can you cut a rectangle into 2 parts of equal area?
Ans: Infinite.
Why is it infinite ways?In any case, how is the cutting line drawn?
Extend the same solution to a rectangular sheet which has a rectangular hole in it. I think this will help you.
Yes Ensie I uploaded a picture. Anyways, I'll put the question simple.
How can you cut a rectangular sheet having a rectangular hole in it to 2 parts of equal area. Use only one cutting line and I think the above hint may help you.
I'm going to post the solution tomorrow.
Replies
I don’t know its answer really, but if I were you I would use “ inverse” for it.
Let me say that I didn’t know the meaning of “upside down”, but when you used it I searched it in the dictionary and I found out that it’s an adverb and it means: “ With the top part at the bottom”.
For example: when we hang a picture on the wall wrongly so that the top is at the bottom. We will say: " The picture is upside down."
I said “norm” was 6 cm, but I meant its base. Sorry I didn’t know its name in English before, but I know it now. Thanks for your saying.
Now please pick up a pen and a paper and draw what I will say.
Please draw a rectangular that its length is 7 and its width is 3. Then put a hole in the bottom of its right side, just like one of your pictures. Draw the length of the hole, 3 and its width 1.
Now we want to make a triangular that its area must be 18. So we can suppose 6 for its base and 3 for its height.
Part 6 cm from upper length of the rectangular from its left side.
Now, please draw a straight line from that place to the bottom angle of the left side of the rectangular.
So, we will have a triangular that is 90 degrees in one of its angles.
Its base is on the upper length of the rectangular and its height is on the left width of the rectangular.
And also, the hole won’t be inside our rectangular.
You have done it well. Thanks for trying. you explained it very well.
At last we all are learning.
But......
Take a rectangular sheet of length 7 and breadth 3 having
a hole of length 2 and breadth 2.
Will your solution work in this case??I think it fails.
Another hint for you friend : Try to make the resultant parts symmetrical(i.e identical). How should be the cutting line??
Thanks
Naresh
But in that condition I will try to make a rectangular instead of triangular. That its length will be 3 (It can be on the width of main rectangular) and its breath will be 17/6. Because in that situation we need 8.5 for every part.
7*3=21
2*2=4
21-4=17
17/2=8.5
In fact I will try to make triangular, square or rectangular with one line.
A picture speaks a thousand words. Both the figures explain about the same puzzle. Don't think they are different puzzles. And yes, we should use only one cutting line. Sorry guys, if you think the explanation is not clear before.However, this is really a good question I came across in one of my interviews. Hope you like it.
In how many ways can you cut a rectangle into 2 parts of equal area?
Ans: Infinite.
Why is it infinite ways?In any case, how is the cutting line drawn?
Extend the same solution to a rectangular sheet which has a rectangular hole in it. I think this will help you.
Cheers
Naresh
How can you cut a rectangular sheet having a rectangular hole in it to 2 parts of equal area. Use only one cutting line and I think the above hint may help you.
I'm going to post the solution tomorrow.
Cheers
Naresh
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