How do you solve this?

ABC is a triangle; XY is a line segment such that XY is parallel to BC intersecting AB at X and AC at Y dividing DeltaABC into two parts equal in area. What is the ratio of BX and AB?

1 Answer
Dec 27, 2017

(BX)/(AB)=1-1/sqrt2

Explanation:

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Given that XY // BC, => DeltaAXY and DeltaABC are similar.
In two similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
Given that XY divides DeltaABC into two parts equal in area,
let area of DeltaAXY be a, => area of DeltaABC=2a,
=> ((AX)/(AB))^2=a/(2a)=1/2
=> (AX)/(AB)=1/sqrt2
=> (BX)/(AB)=(AB-AX)/(AB)=1-(AX)/(AB)=1-1/sqrt2