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#