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