Gopalgang higher hisec 2011 10

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Mehfuj Zahir
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Gopalgang higher hisec 2011 10

Unread post by Mehfuj Zahir » Thu Feb 03, 2011 11:23 pm

Length of all the sides of an isocles triangle are integer valued.If the perimeter is 20 how many ways the triangle can be formed?
Last edited by Mehfuj Zahir on Fri Feb 04, 2011 12:20 am, edited 1 time in total.

Mehfuj Zahir
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Re: Mymensingh higher sec 2011 10

Unread post by Mehfuj Zahir » Thu Feb 03, 2011 11:24 pm

Ans should be 4

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amlansaha
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Re: Gopalgang higher hisec 2011 10

Unread post by amlansaha » Tue Dec 06, 2011 1:45 am

but i think the answer is $8$ .
let $a, a, b$ are the sides of the triangle. so
$2a+b=20$
$a=\frac{20-b}{2}$
there are $8$ possible results of $(a,b)$ [$(9,2),(8,4),(7,6),(6,8),(5,10),(4,12),(3,14),(2,16),(1,18))$]( whereas a, b are positive integers.
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nafistiham
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Re: Gopalgang higher hisec 2011 10

Unread post by nafistiham » Tue Dec 06, 2011 1:29 pm

but,amlan da
Euclid says,
the summations of two sides in a triangle is larger than the other side.

so, the rightmost $5$ combos are incorrect.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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amlansaha
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Re: Gopalgang higher hisec 2011 10

Unread post by amlansaha » Tue Dec 06, 2011 4:11 pm

nafistiham wrote:but,amlan da
Euclid says,
the summations of two sides in a triangle is larger than the other side.

so, the rightmost $5$ combos are incorrect.
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thanx nafis :)
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