## How two altitudes determine the third

Kazi_Zareer
Posts: 86
Joined: Thu Aug 20, 2015 7:11 pm
Location: Malibagh,Dhaka-1217

### How two altitudes determine the third

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
We cannot solve our problems with the same thinking we used when we create them.

aritra barua
Posts: 57
Joined: Sun Dec 11, 2016 2:01 pm

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

### 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