Question

in triangle abc, xy parallel AC and xy divides the triangle into two parts of equal area find the ratio of AX/XB

Answer 1

this is the answer as per the textbook

Answer 2

Given :  in Δ ABC  XY ||  AC  XY divides the triangle anto two parts of Equal area

To find : AX / XB

Step-by-step explanation:

let say area of Δ BXY =  A

then Area of Δ ABC = 2A    

XY || AC

=> Δ BXY ≈ Δ BAC

as we know that ratio of area of similar triangle = (ratio  of sides of similar triangle)²

=>  A /2A  = (BX/AB)²

=> 1/2 =  (BX/AB)²

=> 1/√2  = BX/AB

=> AB /BX = √2

lets subtract  1 from both sides

=>  AB /BX  - 1  = √2 - 1

=> (AB - BX)/BX  = √2 - 1

=> AX/XB = √2 - 1

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