SOLUTION: In ΔABC, X and Y are points on sides AB and BC respectively such that XY parallel to AC and XY divides triangular region ABC into two parts equal in area. Then AX/AB is equal

Algebra ->  Triangles -> SOLUTION: In ΔABC, X and Y are points on sides AB and BC respectively such that XY parallel to AC and XY divides triangular region ABC into two parts equal in area. Then AX/AB is equal       Log On


   

Question 806163: In ΔABC, X and Y are points on sides AB and BC respectively such that XY parallel to AC and XY divides triangular region ABC into two parts equal in area. Then AX/AB is equal to
Answer by mananth(16946) About Me  (Show Source):
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Intriangle;ABC, X and Y are points on sides AB and BC respectively such that XY parallel to AC and XY divides triangular region ABC into two parts equal in area. Then AX/AB is equal to
In triangle AXY & ABC
Angle AXY is congruent to ABC ( corresponding angles)
Angle A is common
By AA test of similarity the triangles
triangle ABC & AXY are similar
Area of Triangle AXY/area of ABC = AX^2/AB^2
But The ratio of areas = 1/2
1/2 = AX^2/AB^2
1/sqrt(2)= AX/AB