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In the adjoining figure, XY is parallel to AC. If XY divides the triangle into two halves with equal area, compute AX/AB.

 

 May 11, 2020
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If the two areas are equal......then  the area of the smaller triangle  =1/2 area of larger triangle

 

Then......the scale  factor  of  the smaller triangle  to the larger  =  1/ √2

 

This  means that  the  height of the  smaller triangle  to  the  height of the larger =  1 / √2

 

Since both triangles are  similar  this also means that   BX  / AB  =1 / √2

 

Therefore.....AX  =  AB  - BX   =    √2 - 1    

 

Therefore

 

AX / AB  = [ √2 - 1  ]  / √2    

 

 

cool cool cool

 May 11, 2020

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