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### How two altitudes determine the third

Posted: Fri Feb 03, 2017 5:26 pm
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

### Re: How two altitudes determine the third

Posted: Wed Feb 22, 2017 2:21 pm
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.

### Re: How two altitudes determine the third

Posted: Fri Feb 02, 2018 2:17 am
You can use the triangle inequality to get the answer.

### Re: How two altitudes determine the third

Posted: Mon Feb 19, 2018 7:26 pm
This is the problem of BdMO National Secondary 2014/8