Correct option is B
In triangle ABC, line segment XY is parallel to side AC and divides the triangle into two parts of equal areas.
We are to find the ratio of AX to AB.
Concept used:
When a line is drawn parallel to the base of a triangle and divides it into two equal areas, it forms a smaller triangle (BXY) at the top with half the area of the larger triangle (ABC).
Since both triangles are similar (because XY ∥ AC), the ratio of sides will be the square root of the ratio of areas.
Solution:
Area(BXY) : Area(ABC) = 1 : 2
=> (AX / AB)² = 1 / 2
=> AX / AB = 1 / √2
=> AB / AX = √2 / 1 => AX : AB = 1 : √2
Now rationalizing:
1 : √2 = √2 : 2
Correct answer is (b) √2 : 2.
