BdMO National Junior 2008/6

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
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Joined:Sat Dec 09, 2017 1:32 pm
BdMO National Junior 2008/6

Unread post by samiul_samin » Sun Feb 24, 2019 10:02 am

The diagonals of a rectangle exceeds the length by $2$ $cm$.If the width of the triangle is $10$ $cm$,find the length.

samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm

Re: BdMO National Junior 2008/6

Unread post by samiul_samin » Sun Feb 24, 2019 1:39 pm

Answer:$\fbox {24}$

Solition:
Let \[Length=a\]
\[width=b=10\]
\[diagonal=d=a+2\]
So,
\[d=\sqrt{a^2+b^2}\]
\[\Rightarrow a+2=\sqrt{a^2+10^2}\]
\[\Rightarrow (a+2)^2=a^2+100\]
\[\Rightarrow a^2+4a+4=a^2+100\]
\[\Rightarrow a+1=25\]
\[a=24\]

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