Question

Help in solving geometry

Answer 1

Answer:

Therefore

$x=15\\\\y=4$

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

$\frac{AM}{MF}=\frac{AE}{EC}$.....Basic Proportionality Theorem

substituting the values we get

$\frac{x}{5}=\frac{18}{6}\\\\\therefore x=3\times 5=15$

Similarly,

In Δ AFC

ME || FC

$\frac{AD}{DB}=\frac{AM}{MF}$......Basic Proportionality Theorem

substituting the values we get

$\frac{12}{y}=\frac{15}{5}\\\\\therefore y=\frac{12}{3}=4$

Therefore

$x=15\\\\y=4$