Question

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?

Answer 1

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

Explanation:

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`