Question
Fri February 13, 2009 By:

triangles

Expert Reply
Sat February 14, 2009

Suppose that each of the equal areas is x units.

So areaof the smaller triangle BXY =x units.

and

 area of the larger triangle BAC= x+x= 2x units

Now ,

 we are given that the line XY  is paralle to the side AC of the triangle ABC.

So,

the two triangles can be proved similar by AA rule.

Since

 triangle BXY is similar to triangle BAC,

we get

 area( triangle  BXY)/ area( triangle BAC)= ratio of squares of correspondng sides

so,

 

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