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A 5 meter long wire is cut into two pieces. If the longer piece is the

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avigutman
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Re: A 5 meter long wire is cut into two pieces. If the longer piece is the [#permalink] New post   21 Oct 2021, 04:38
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kskumar wrote:
avigutman please add your way of solving the above question. I have tried to solve it by ratios but I am little bit confused.


kskumar the square will have an area greater than 1 if its perimeter is greater than 4, so rephrase the question:
What's the probability that the longer piece (which by definition is longer than 2.5 and shorter than 5) is longer than 4.

So, analogous question:
If 2.5﹤x﹤5, what's the probability that x﹥4?

*Note: the length of the range between 2.5 and 5 does NOT depend on whether the range is inclusive or exclusive. See page 29 of my book for more on that.

Well, the total range that we'd be happy with is length 1 (between 4 and 5), out of a total possible range of 2.5 (between 2.5 and 5), so the correct answer is 1/2.5. Expand by a factor of 2 and get 2/5.
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Re: A 5 meter long wire is cut into two pieces. If the longer piece is the [#permalink] New post   14 Apr 2022, 05:52
Hi,

this question really is not that hard.

Given that x is the length of the rope, and we always take the longer piece, we can infer that 2.5<= x < 5.
Now, we have to form the perimeter of a square with x. Perimeter is given by 4a=P with a being one side's length of the sqaure. We know in total:

4a=x
a=x/4

-> 2.5/4 <= x < 5/4
0.625 <= x < 1.25

For A=a^2>1 -> a>1. Our range is approximately 0.6, and less than 0.25 values fulfill our requirement -> approximately 40%
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Re: A 5 meter long wire is cut into two pieces. If the longer piece is the [#permalink] New post   06 Dec 2022, 05:53
Was trying to explain this question to someone on the YouTube community section. When I realised this

Think of this situation as if you were playing darts with this wire and the wire is cut at where ever the dart lands ( the question stem says the wire is cut at an arbitrary point )

L ————————————-———— R
|1cm|_______|3cm|_________|1cm|

As long as the dart lands on either of the 1cm lengths we get our required result

So now we have 2cm of the total 5cm where making a cut will yield the required result

Hence 2/5 (e)

Posted from my mobile device
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Re: A 5 meter long wire is cut into two pieces. If the longer piece is the [#permalink] New post   14 Dec 2022, 06:51
Hi,

So I got the correct answer but not on my first attempt. I used a slightly different and much longer method for my first attempt. I am unable to understand why that method is wrong. Would request you to bear with me and help me out. Bunuel chetan2u yashikaaggarwal

Let the length of the longer piece be X.
5/2<X<5
5/8<Perimeter<5/4
25/64<Area<25/16
Since it is mentioned that what must be the probability for Area to be greater than 1
Total Sample Space=25/16-25/64=75/64
Fav Outcomes=25/16-1=9/16
Hence Probability=9/16 divided by 75/64= 12/25
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Re: A 5 meter long wire is cut into two pieces. If the longer piece is the [#permalink] New post   14 Dec 2022, 08:11
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szcz wrote:
Hi,

So I got the correct answer but not on my first attempt. I used a slightly different and much longer method for my first attempt. I am unable to understand why that method is wrong.


I explained why your method is incorrect on the previous page -- we're choosing a random length, not a random area, and lengths and areas aren't distributed in the same way. You can just imagine taking a random side length for a square between 0 and 10 (including decimal numbers). The areas of these squares will range from 0 to 100, but the probability you get an area greater than 50 is not 1/2; you'd need to pick a number greater than roughly 7.07 to get an area that large, so the probability is less than 3/10.

If you use your method, but don't square things before finding your numerator and denominator, you'll get the right answer.
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Re: A 5 meter long wire is cut into two pieces. If the longer piece is the [#permalink] New post   14 Dec 2023, 15:26
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Re: A 5 meter long wire is cut into two pieces. If the longer piece is the [#permalink]
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