Answer:
Therefore
[tex]x=15\\\\y=4[/tex]
Step-by-step explanation:
Consider the Figure as shown below where
DE || BC
i.e ME || FC
AD = 12
AE = 18
MF = 5
EC = 6
To Find:
AM = x = ?
DB = y = ?
Solution:
We Know that
Basic Proportionality Theorem:
Basic Proportionality Theorem states that "If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".
In Δ AFC
ME || FC
[tex]\frac{AM}{MF}=\frac{AE}{EC}[/tex].....Basic Proportionality Theorem
substituting the values we get
[tex]\frac{x}{5}=\frac{18}{6}\\\\\therefore x=3\times 5=15[/tex]
Similarly,
In Δ AFC
ME || FC
[tex]\frac{AD}{DB}=\frac{AM}{MF}[/tex]......Basic Proportionality Theorem
substituting the values we get
[tex]\frac{12}{y}=\frac{15}{5}\\\\\therefore y=\frac{12}{3}=4[/tex]
Therefore
[tex]x=15\\\\y=4[/tex]
