Brain Teasers
Paper Room
A room is 12' x 8' when it is designed on paper. You decide to make it square, and take 2 feet off the length and add it to the width to make it 2 feet wider. The room is now 10' x 10'. The total square footage of the first room was 96sq feet, the total footage of the second room is 100sq feet. Where did the extra 4sq feet come from?
Answer
The 2' taken off the first room is 2' x 8' for a total size of 16sq feet. To add it onto the second room you make it 2' x 10', which is 20sq feet. That's the extra 4 sq feet.Hide Answer Show Answer
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Comments
The solution merely begs the question. One could ask regarding the solution where does the 4 feet come from when removing the 2X8 segment and "adding" it back as a 2X10 segment? The simple fact is that as perimeter stays constant, area may vary. I think it is innaccurate to characherize the area as 'coming from anywhere'. (If the extra area "came from anywhere" it came from the net portion of the ground not previously surrounded by the perimeter.)
it really doesn't require that much thought. specifics and details aren't really needed in this problem. though that is a good point.
The sum of the sides is 20, (8*12) or (10*10). A room 19*1 has 19sq ft; 18*2 has 36sq ft; 17*3 has 51sq ft; 16*4 has 64sq ft, and as we have seen, 8*12 has 96sq ft. So, the nearer the length and breadth are to one another, the larger the area!
i agree with ymiroc
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