BdMO National Junior 2008/6
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
The diagonals of a rectangle exceeds the length by $2$ $cm$.If the width of the triangle is $10$ $cm$,find the length.
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- Posts:1007
- Joined:Sat Dec 09, 2017 1:32 pm
Re: BdMO National Junior 2008/6
Answer:$\fbox {24}$
Solition:
Let \[Length=a\]
\[width=b=10\]
\[diagonal=d=a+2\]
So,
\[d=\sqrt{a^2+b^2}\]
\[\Rightarrow a+2=\sqrt{a^2+10^2}\]
\[\Rightarrow (a+2)^2=a^2+100\]
\[\Rightarrow a^2+4a+4=a^2+100\]
\[\Rightarrow a+1=25\]
\[a=24\]
Solition:
Let \[Length=a\]
\[width=b=10\]
\[diagonal=d=a+2\]
So,
\[d=\sqrt{a^2+b^2}\]
\[\Rightarrow a+2=\sqrt{a^2+10^2}\]
\[\Rightarrow (a+2)^2=a^2+100\]
\[\Rightarrow a^2+4a+4=a^2+100\]
\[\Rightarrow a+1=25\]
\[a=24\]