Point B ∈ |AC| so that AB:BC=2:1. Point D ∈ |AB| so that AD:DB=3:2. Find AD:DCThanks plz answer I don’t get it

Accepted Solution

Answer:5:4Step-by-step explanation:If point B divides the segment AC in the ratio 2:1, then AB=2x units and BC=x units.If point D divides the segment AB in the ratio 3:2, thenAD=3y units and DB=2y units.Since AD+DB=AB, then[tex]3y+2y=2x\\ \\5y=2x\\ \\y=\dfrac{2}{5}x[/tex]Now,[tex]AD=3y\\ \\DC=DB+BC=2y+x=2y+\dfrac{2}{5}y=\dfrac{12}{5}y[/tex]So,[tex]AD:DC=3y:\dfrac{12}{5}y=15:12=5:4[/tex]