If the lengths of two altitudes drawn from two vertices of a triangle on their opposite sides are $2014$ and $1$ unit, then what will be the length of the altitude drawn from the third vertex of the triangle on its opposite side?
Source: BdMO National 2014
How two altitudes determine the third
 Kazi_Zareer
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How two altitudes determine the third
We cannot solve our problems with the same thinking we used when we create them.

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Re: How two altitudes determine the third
Let,ABC denote a right angled triangle.Let,the sides be 2014,1 and y units.Then the area of the triangle will be 1007 sq units.If we construct another altitude x in length,then the area will be xy/2 units.Then,we apply an equation,xy/2=1007;then x results in 2014/√(2014^2+1) units which denotes the length of the 3rd altitude.
 samiul_samin
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Re: How two altitudes determine the third
You can use the triangle inequality to get the answer.
 samiul_samin
 Posts: 1007
 Joined: Sat Dec 09, 2017 1:32 pm
Re: How two altitudes determine the third
This is the problem of BdMO National Secondary 2014/8
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